Rocchini

Welcome!

Hello, Rocchini, and welcome to Wikipedia! Thank you for your contributions. I hope you like the place and decide to stay. Here are some pages that you might find helpful:

• The five pillars of Wikipedia
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• How to write a great article
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I hope you enjoy editing here and being a Wikipedian! Please sign your name on talk pages using four tildes (~~~~); this will automatically produce your name and the date. If you need help, check out Wikipedia:Questions, ask me on my talk page, or ask your question and then place {{helpme}} before the question on your talk page. Again, welcome!  Oleg Alexandrov (talk) 03:41, 8 August 2007 (UTC)

Rose

Hey Rocchini. Just wanted to say "well done" with that graphic for the Rose. It looks really nice. Cheers, Doctormatt 08:36, 6 November 2006 (UTC)

Cat

Chapeau Claudio! Nice contribution to the article Arnold's cat map. JocK 19:14, 9 November 2006 (UTC)

Once more a request for your artistic talents... You might be interested in another visualisation of the chaos occuring in simple discrete maps like Arnold's cat map. If you take - say - a 50 x 50 integer grid, and start iterating the cat-map on that grid to obtain the various closed trajectories, and color each distinct trajectoru differently, a nice colourful plot is obtained. See http://base.google.com/base/a/jkoelm/1121639/6838743187121338456 for a similar picture for another integer 2D-map (as you can see: my graphics skills aren't anywhere close to yours). Cheers, JocK 21:18, 8 August 2007 (UTC)

Dipole graph

I just wanted to thank you for the image you added to Dipole graph. I've been meaning to make one but couldn't find a nice tool to do it with--and my skill at MS Paint isn't sufficient for the task. Do you mind if I ask what tool you used to make the image? I'd like to be better prepared in the future. --Sopoforic 05:00, 28 November 2006 (UTC)

Spherical cap

Excellent job on the image, it helps the article, and I appreciate it. The same for your other math images. —Ben Brockert (42) 05:45, 29 November 2006 (UTC)

SVG

I asked previously which tools you use to create images, and you recommended Inkscape, which I have found quite satisfactory. I notice, though, that you've been uploading your images in GIF format. If you've still got the SVGs you used to make those images, you should upload them directly, since they'll look much nicer, and be more useful besides. If you've not got them, you should still keep it in mind for the future. Thanks for your work, in any case. --Sopoforic 01:46, 10 January 2007 (UTC)

SVG glitch

I've encountered a problem with some of your SVG files; it seems that values with under four digits (such as 50.0) are recorded in the files with a space preceding the value (so instead of "50.0", you get " 50.0"). I don't know about other browsers, but in Firefox, this causes the object with said value as an attribute to be incorrectly parsed. Three of your files that I know have this effect are Image:120-cell_petrie_polygon.svg, Image:600-cell_petrie_polygon.svg, and Image:E8_graph.svg. I have not yet checked if more of your files have a similar problem. Cat Megex (talk) 13:54, 17 June 2009 (UTC)

UPDATE: The problem is indeed not limited to the above-listed images, and it's for any value with less digits than the values with the highest number of digits in the set of objects. However, it does not seem to happen with the Inkscape-generated images. Cat Megex (talk) 15:56, 18 June 2009 (UTC)

Honeycomb images

Hi! Great images for the uniform polychorons. I've been expanding the Coxeter-Dynkin diagram. I also saw your rcent nice cell-uniform tessellation at Disphenoid tetrahedral honeycomb. I'm wondering if you could make a similar tessellation image for the dual of: Cantitruncated cubic honeycomb. I don't have a name for it, but this tetrahedral space-filling dual should represent the fundamental domains for Coxeter's S₄ infinite group. Does this make sense? I'm still getting the hang of things. Thanks for considering! Tom Ruen 06:24, 24 January 2007 (UTC)

Hey! I have to agree these images are amazing, I'm using the Order-3 for my background. I was just wondering what program you used, it looks very professional and at the moment all I'm using is GIMP and Inkscape. Aragan Jarosalam

I use my mathematical C++ class library wich exports the results in vrml format (for preview) and POV Ray format (for final version of images). (Quasi) all images of my gallery are done with my library. Rocchini.

excellent image at braid theory

I will certainly remember you for the next time I need a nice image! --C S (Talk) 13:38, 28 January 2007 (UTC)

Hyperbolic tilings

Hi Rocchini!

Great new images on Hyperbolic great cubic honeycomb!

I've also been wishing to expand the 2d hyperbolic tiling as well, but I don't have software that can generate the uniform duals: See blanks at List_of_uniform_planar_tilings#Uniform_tilings_in_hyperbolic_plane

They are all similar topology to the Euclidean tilings. Coloring the duals is unclear since they have identical faces. I wouldn't even mind if they are single-colored faces with dark edges.

Maybe they are "too easy" for you, but it thought I'd ask. I'm glad for where ever you can help!

Tom Ruen 23:15, 5 February 2007 (UTC)

for a moment I have made the common image Order3_heptakis_heptagonal_til.png ,

but I not undestand how to insert in the List_of_uniform_planar_tilings#Uniform_tilings_in_hyperbolic_plane page. Because in the original tilining the color is per face, in the dual tiling I have colored the surface per vertex.

Thanks Rocchini! Sorry on the template confusion. The source (database) is at: Template:Uniform_hyperbolic_tiles_db. I added it for your example. I don't mind how it is colored, although best to have a full set of vertex-colorings if you could repeat them all that way. Thanks again! (I also linked image at Triangular_tiling) Tom Ruen 21:07, 7 February 2007 (UTC)

Can you make the nonreflective snub form duals? Explained a bit here for a flat tiling: Snub_square_tiling - creating an omnitruncation and then delete alternated vertices? Don Hatch does this in an interesting way in an Applet at Hyperbolic Planar Tesselations by Don Hatch but no colors. Tom Ruen 21:13, 7 February 2007 (UTC)

Wonderful work! Thanks! I thought tonight the (5 4 2) family would be a useful example as well betond the (4 4 2) tilings. Could you try those as well? I left open image links at:List_of_uniform_tilings#.285_4_2.29_family. Tom Ruen 07:42, 10 February 2007 (UTC)

Hi Rocchini. Thanks again for your great images. I saw I made a mistake on omnitruncated dual tiling names, not a kis operation. I replaced it with term bisected for (5 4 2) group (Image:Order-4 bisected pentagonal tiling.png) and will update the rest when I have time. So at least you can continue on List_of_uniform_tilings. Thanks again! Tom Ruen 02:36, 14 February 2007 (UTC)

Wow! All so beautiful! I found one more family to complete a good demonstrational survey of the hyperbolic tilings

Euclidean --> hyperbolic

(6 3 2) --> (7 3 2) - Hexagonal/heptagonal (DONE)

(4 4 2) --> (5 4 2) - Square/pentagonal (DONE)

(3 3 3) --> (4 3 3) - Triangular/square (started)

What do you think of the last one? I just linked (4 3 3) at List of uniform tilings. Tom Ruen 23:05, 15 February 2007 (UTC)

I suppose that a nice coloring rule of duals is related to some property of the tessellation (Symmetry group?), but i not understand how. User:rocchini 20 February 2007 (UTC)

I don't have a simple rule for coloring dual faces by symmetry. Since they are all face-transitive, the lowest coloring is ONE color! There's probably many colorings for each limited by the symmetry orders. It is nice when all neighboring faces are different colors. Your choices have been beautiful! :) Tom Ruen 18:06, 20 February 2007 (UTC)

A small issue: The Image:Uniform dual tiling 433-t01.png tiling is a wonderful 3-color pattern, but incompletely applied near edges. I tried to fix it but couldn't do it nicely with antialiasing. Tom Ruen 19:14, 20 February 2007 (UTC)

Hi Rocchini. Looks like you're busy, me too! I just thought to add a simple white tiling image for the final snub (Image:Uniform dual tiling 433-snub.png) would be great whenever you have the time. Thanks! Tom Ruen 07:46, 28 February 2007 (UTC)

Thanks for finishing the last hyperbolic dual snub tiling. I had one other snub I couldn't make easily on a larger uniform survey (without duals) at Wythoff symbol - need Image:Uniform_tiling_443-snub.png similar to Image:Uniform_tiling_433-snub.png. I left an open link for it at Wythoff symbol.

I'm also very glad for more 3D hyperbolic tilings too! It would be fun to try some truncated versions, like table at Truncation_(geometry)#Truncation_in_polychora_and_honeycomb_tessellation ... probably need an "inside perspective" to show them. Tom Ruen 23:52, 1 March 2007 (UTC)

I have worked 5 days (and povray 12hours) for this hyperbolic awful image. I try to remake it in the next week.

I don't know how you do any of it, and it all seems beautiful to me. Much glad for your work. Peace and thank you! Tom Ruen 10:01, 2 March 2007 (UTC)

Image:Cayley graph formula 2 4.gif listed for deletion

An image or media file that you uploaded or altered, Image:Cayley graph formula 2 4.gif, has been listed at Wikipedia:Images and media for deletion. Please look there to see why this is (you may have to search for the title of the image to find its entry), if you are interested in it not being deleted. Thank you. – Tintazul ^msg 23:42, 20 February 2007 (UTC)

I have to add: you make such wonderful images for Wikimedia! Thank you for that. Although I should ask, if whenever possible, you could make those images available in vector format. I use Inkscape, which ias fairly easy to use. This is the case now: I have redrawn your image completely in SVG, keeping to the original colours and structure as much as possible. If you have any doubts, please contact me. Ciao! – Tintazul ^msg 23:42, 20 February 2007 (UTC)

Thanks for this work! I generate the original image via agg graphics library (this library save only raster image), and i am too much lazy to remake this image.

Hypercube graphs?

Hi Rocchini! If you'd like a little challenge for your to-do list, I'd like to flesh out some graphs for the n-hypercubes, like done for the simpler families: simplex and cross-polytope. Mathworld offers some graphs, although I do NOT know the pattern for adding "rings" of new vertices - maybe lots of possibilities? See:[[1]]. Well, just thought I'd point it out. I could try myself sometime since graphics is easy, but theory of positions a mystery. I added a hexeract stub along with penteract. Hey, another source of graphs [2] - maybe they're actually certain views of an orthogonal projection? Tom Ruen 06:39, 16 March 2007 (UTC)

Wow! Thanks! You're fast! If you're interested another fun class are the demihypercubes. I added a graph column there. Tom Ruen 19:57, 16 March 2007 (UTC)

E6,7,8 graphs?

Hi Rocchini! Thanks for the hypercube/demi graphs. What do you think of the E6 polytope {3^2,2,1}, E7 polytope{3^3,2,1}, E8 polytope {3^4,2,1} graphs? I have pictures from a book, but don't really understand the structures. Can you reproduce these in SVG? Image:E6_graph.png, Image:E7-8 graphs.png Tom Ruen 08:40, 26 March 2007 (UTC)

Example of E8 drawing at: [3] (dense!) Tom Ruen 01:44, 27 March 2007 (UTC)

As you see, I have not understood the argument. How to compute the root adjacency? User:Rocchini 2007-04-26.

Hey Rocchini, no problem. I don't know how to compute them either. I just hoped you might. :)Maybe I can find some source code that plots them sometime. Thanks again, and keep up with the great graphs and pictures! Tom Ruen 16:47, 26 April 2007 (UTC)

This is e6, e7, e8 in svg format Image:E6_graph.svg, Image:E7_graph.svg, Image:E8 graph.svg. It is correct? User:Rocchini 2007-06-04

Thanks! Looks very good to me. I'm very glad for these nice additions. I added labels to the article picture captions. Tom Ruen 16:19, 4 June 2007 (UTC)

Kudos

Kudos for all your wonderful images! (from an old friend that has just discovered you as a wikipedian) ALoopingIcon 23:31, 16 April 2007 (UTC)

Moving sofa problem

Hi Rocchini, you might want to have a look at Moving sofa problem. It would be great if you could create an animated gif that shows a 'telephone shaped' sofa moving through a right-angle corridor. I don't think such a graphics is available anywhere on the internet. Cheers, JocK 17:46, 25 May 2007 (UTC)

I try this: , User:rocchini 28 may 2007 (UTC).

Again a fantastic piece of graphics! Many thanks, JocK 10:58, 28 May 2007 (UTC)

Complex analysis

Thank you for the awesome picture at Complex analysis. It is just great! Oleg Alexandrov (talk) 03:41, 8 August 2007 (UTC)

I second that! I modified your code a bit and used it to visualize some of my own complex functions. Thanks. —Preceding unsigned comment added by 69.138.148.85 (talk) 06:30, 16 February 2011 (UTC)

I also want to thank you for sharing the idea of the coloring scheme (so much nicer than just using sawtooth functions for adding grey barriers)! While learning for an exam in complex analysis I created a very basic interactive complex function plotter using your scheme. If you or anyone else is interested in it you can find it at http://sourceforge.net/projects/gcfp/ . --95.118.131.182 (talk) 15:41, 2 March 2012 (UTC)

A further comment on pictures

As many people have noticed, you are creating really awesome pictures. I have a suggestion. Would it be possible for you to include the source together with each picture? I, for example, would be very interested in learning from you, and I am sure I am not the only person. Thanks. You can reply here. Oleg Alexandrov (talk) 06:39, 8 August 2007 (UTC)

Thanks for comments and suggestion. I have the same idea, but this "thing" is not so easy. The "source" of each image is a mix of C++ source code plus external library (like AGG graphics), shell script, Blender and POV-Ray scripts, manual adjustments ans so on. My idea is to make, for each image, a "making of" page of the image. I do not know which location is the better place for these pages (wikipedia or a private personal site). I am working on. Rocchini 08:55, 9 August 2007 (UTC)

Any of this information can go on the picture page, for example, on commons:Image:Color complex plot.jpg, under the picture itself. Of course, if it is a lot of work to make the source public, and if you prefer to make new pictures rather than spend time writing about how you made the current pictures, that is understandable. Cheers, Oleg Alexandrov (talk) 16:09, 9 August 2007 (UTC)

Hyperbolic sector

Thank you Rocchini for producing an appropriate graphic for hyperbolic sector. I have also used it on hyperbolic angle. I find your gallery spellbinding. Great art and science fused to one. Beginners in things hyperbolic will benefit from the hyperbolic sector graphic. with much appreciation, Rgdboer 22:28, 13 September 2007 (UTC)

Now you have done even more good work at Ultraparallel theorem and Hyperbolic coordinates. I would like to put a caption on the hyperbolic coordinate image, but it should indicate the level curve geometric means and the separation of radial lines by a uniform hyperbolic angle. The way they bunch up near the asymptote gives the impression that is appropriate for hyperbolic angle. Today there is no diagram at hyperbolic angle due to a recent unfortuate sequence of edits. The diagram there should be more detailed than the one at hyperbolic sector, since the article is developing the measure concept. I would suggest using the point (1.39561242, .7165313) as a basic unit from (1,1). Since this pair corresponds to the cube root of e, the area of the sector is one-third wing, if we take the basic area one angle as defining a wing. Degrees and radians are familiar circular angle measures, and the centuries of use of circular angle has made these units common language. To date, I know of no initiative to introduce a named unit to refer to a hyperbolic angle, yet in cases such as this a named unit would be useful. Without such language, one can speak of the powers of the 1.3956 pair, and about ten of these will fill an octant, getting dense near the asymptote. If you used some other hyperbolic angle unit to generate the image at hyperbolic coordinates, it would be good to see it in a caption.Rgdboer (talk) 23:30, 20 May 2008 (UTC)

Thanks for ctr. octag. # img.

Just wanted to say thanks for your Image:Centered octagonal number.svg on behalf of WikiProject Numbers. It looks very nice. Thanks for the image. PrimeFan 23:51, 7 October 2007 (UTC)

Image:Edge contraction.svg

Hello, I have replaced the arrows of this image with hand-drawn arrows because the arrowheads did not render properly due to a render-bug/limitation in wikipedia. If you want to see the bug you can revert to the old version at commons:Image:Edge_contraction.svg#file history. It does not look as good now, but at least it now shows properly in the article. ssepp^(talk) 16:54, 21 October 2007 (UTC)

Thank you for refinements! Rocchini 13:00, 22 October 2007 (UTC)

Image:Cayley's formula 2-4.svg

Hello, I have uploaded a new version of this image. In the old version ([4]) if we look at the trees with 4 vertices, then, referring to the trees in matrix notation, tree (1,1) and (2,2) are both red-yellow-green blue, and trees (1,3) and (3,2) are both blue-red-yellow-green. Trees with red-blue-green-yellow and yellow-red-blue-green were missing. In the new version I have fixed this. I hope it is ok now, it is easy to get confused working with this :). ssepp^(talk) 17:44, 21 October 2007 (UTC)

Thank you for refinements! Rocchini 13:00, 22 October 2007 (UTC)

Color Complex Plot Image

I was wondering what program you use to create your image for the Complex Numbers page. I've been looking for something that could plot things of that nature for quite a while, and I would be greatly appreciative if you could help me. Vjasper 20:49, 23 October 2007 (UTC)

I have added to image page the C++ source code for generating this image. You may change the FUN function to plot another complex function. Rmi, Rma, Imi, Ima represents the function domain. Rocchini 06:39, 25 October 2007 (UTC)

Thx for great image. Your method ( creating PPM file) is probably the simplest ( and effective) method of crating 2D 24 bit color graphic. I was looking for this for years and now I have found. Thx. I have made a simple example about it in Polish wikibook. Maybe it should be in new wbook about graphic/c ? Do you know something about flo files ? Regards --Adam majewski (talk) 07:58, 15 December 2007 (UTC)

Isn't there something wrong with the picture? The function should have 3 zeros and 2 poles and not the other way around. 176.83.100.213 (talk) 12:07, 12 October 2012 (UTC)

I think that this image is somehow wrong... It should be vertically mirrored and I do not think that the radius is periodical like the image indicates. I wrote a program, and it produces this image: (I also reproduced it with Mathematica using this code and it looks similar...)

— Preceding unsigned comment added by Dux361 (talk • contribs) 10:54, 11 February 2013 (UTC)

Yes, you're right, the correct version is the Jan Winnicki's one: . Rocchini (talk) 13:12, 11 February 2013 (UTC)

Hello Rocchini, I've developed this demo based on the domain mapping function I found on your pages: http://2π.com/14/visualising-complex-functions Are you the original author of this mapping? I would also enjoy your feedback on the HCL mapping I added. Thanks! 2001:980:A3ED:1:CD4F:E59:8032:C751 (talk) 23:31, 29 August 2014 (UTC)

Art gallery problem

Hello, I thought you might find it interesting to create an image for this article: Art gallery problem. Arthena 22:30, 29 October 2007 (UTC)

I try first sample image . Rocchini 16:16, 30 October 2007 (UTC)

That's beautiful! Thank you! Just one thing: I think the bottom of the middle bottom room should just be green, not cyan, since the blue camera does not reach there. In other words, the right blue camera lacks a horizontal vision line. Arthena^(talk) 21:59, 30 October 2007 (UTC)

Argh! You have good eyes. Rocchini 16:41, 31 October 2007 (UTC)

Angle of parallelism

Thank you Rocchini for getting us a graphic on angle of parallelism. This old idea in geometry is so useful but illusive to those without a model to work on. You have brought the topic out of the shadows. Your contribution is a valuable scientific illustration. Rgdboer 20:37, 15 November 2007 (UTC)

Hypercubes and demihypercubes and 2n-gonal symmetry

Hi Rocchini. The new E8 animation graphics online [5] have inspired me to look at graphing the higher regular/uniform polytopes again.

I've not been successful yet, but thinking the n-hypercube ought to be orthogonally projectable into a regular 2n-gon. Just like the square (2-cube) is a 4-gon, cube (3-gon) projects in a hexagon, hypercube (4-cube) projects in an octagon, etc. This "projection" envelope represents a sort of zig-zag n-space path "circumference" around the figure. Similarly the n-demihypercube (hypercube with alternate vertices deleted) ought to be projectable into a regular n-gon. Well, the hard part is getting the correct "view plane" for this symmetry. The projections may not be "perfect" since there's overlapping vertices on the plane, but still nice for their symmetry, if it can be done.

The closest example I can find is on Mathworld [6], unsure how the graphs are made, and I don't think they are all pure projections, but maybe close.

Anyway, so far I just rewrote a n-cube generator, and can extend to make n-demicubes. I'd really like to try to get the n-cube/n-demicube graphs to correspond to each other (half the vertices in the second). Maybe I'll succeed, or maybe not.

If you'd like to try too, maybe you can follow my suggestions above and see if you can find a projection plane that has this 2n-gonal symmetry. I'll tell you if I make any progress!

Thanks! 20:16, 27 November 2007 (UTC)

You need a mathematical image? Ask me!

Can you draw boundaries of hyperbolic components of Mandelbrot set ? --Adam majewski (talk) 17:16, 24 January 2008 (UTC)

I don't know what is an "hyperbolic component", do you could indicate to me some information sources? Rocchini (talk) 15:56, 29 January 2008 (UTC)

I thought about something like that :

http://facstaff.unca.edu/mcmcclur/professional/CriticalBifurcationPP.pdf see page number 9

or

http://departments.ithaca.edu/math/docs/theses/whannahthesis.pdf see page 12--Adam majewski (talk) 19:27, 29 January 2008 (UTC)

I have made image : [Componens]. --Adam majewski (talk) 13:32, 31 August 2008 (UTC)

Could you make the dual of this? http://upload.wikimedia.org/wikipedia/commons/0/04/633_honeycomb_one_cell_horosphere.png So, basically, the horosphere that results from 6 triangles meeting at a vertex to form a hyperbolic polyhedron. Thanks! — Preceding unsigned comment added by 71.70.207.113 (talk) 23:21, 19 April 2015 (UTC)

Your images

Hey, I stumbled upon some of your graphics, and I have to say, great job! Just a quick question... what program do you use to make your images? --pbroks13^talk? 05:36, 4 April 2008 (UTC)

See Honeycomb images Color and Complex Plot Image source for reponse.

Kochanek–Bartels spline svg

You accidentally labeled 0.5 "1.5" in the Kochanek–Bartels spline illustration. I figured it would be easier for you to correct it than for me to learn how to use a vector editor. Nice illustration in any case!

Floodyberry (talk) 03:16, 27 May 2008 (UTC)

Mathematical Shapes

Hey! Got any good 11-celled Hendecatopes? PS You may like this userbox:

This user's favorite shape is E8.

{{User:Wyatt915/Userboxes/E8}}

Wyatt915? 22:05, 6 June 2008 (UTC)

• Nothing better than the simplex graph since it can't exist in real space below 10-space: Tom Ruen (talk) 22:22, 6 June 2008 (UTC)

Dunce hap

I really enjoy your work, congratulations! The dunce hat animation you did is pretty good. However, it has been done two years ago, so you could perhaps build a better version with more experience and better software. Indeed, it would be nice if the animation flowed smoothly, and once all the edges are identified, the hat rotated in space to reveal more of the structure. Cheers, Randomblue (talk) 00:59, 14 June 2008 (UTC).

Safari rendering anomaly on new svgs

Your new Higman Sims graph illustrations are very nice (though I think someone will now have to update the wikipedia article to explain the construction). The "parts" image is particularly helpful, as it shows how "simple" the graph is.

Just for your information: the SVG images render very poorly in Safari. This is not a big deal for wikipedia, because wikipedia converts SVG to PNG in articles.

I looked at your SVG, and they seem extremely clear and correct. I think this must be some sort of Safari bug? JackSchmidt (talk) 14:24, 19 June 2008 (UTC)

Congrats!

		The Graphic Designer's Barnstar
		Your Images are some of the best that I have ever seen! Wyatt915? 21:15, 19 June 2008 (UTC)

Petrie polygons

Hi Rocchini,

I added a new article Petrie polygon which contains the basics for the regular polytope graphs. They're all based on orthographic projections, and the Petrie polygon is a regular polygon bounding the graph. Perhaps you could see if you could make some more figures with this information? I hand-traced one for the 24-cell from Mathworld, and took low resolution bitmaps from Mathworld for 120-cell and 600-cell. Mathworld also has graphs on the hypercubes which I can't quite yet reproduce. Anyway, I think I've enumerated all the convex regular polytopes of interest. Any help in adding more as SVG is appreciated! :) Thanks! Tom Ruen (talk) 04:00, 27 July 2008 (UTC)

Great start with the demipenteract image! Thanks! Tom Ruen (talk) 19:41, 28 July 2008 (UTC)

The orthographic projection direction are hard to find! I have found the 600-cell. Rocchini (talk) 09:36, 1 August 2008 (UTC)

And now the 120-cell. Rocchini (talk) 10:08, 1 August 2008 (UTC)

Wow, you're astounding. Definitely hard - I've thought about an iterative process to identify the Petrie polygon edges and do axial rotation search to maximize their distance from the center for the higher dimensions, but not brave enough to try. Even 4D figures have too many degrees of freedom for my controls to get there. I'm so glad you can do it.

Also I have tried many ways: the last one is a maccaroni-solution: given Q the number of vertices on the resulting polygon, I find all the subsets of D vertices which are connected (forming the first part of petri polygon), then I try to solve the linear system which projects this subset into the first D petri vertices. If the linear system has a solution then I print the relative parameters. Finally, I choice a set parameters by hands. The source code is something like this:

User_talk:Rocchini/data Rocchini (talk) 07:14, 18 August 2008 (UTC)

Not even Coxeter's books have all these diagrams! But if you can do more, this is great stuff! Maybe we can get a featured article eventually, to show case your great work! Tom Ruen (talk) 18:21, 1 August 2008 (UTC)

I must really thank you for all the work's arguments that you give me. Rocchini (talk) 07:14, 18 August 2008 (UTC)

Great work! I'm so glad you've figured this out so well. I'm sure it was a lot of work. I compared the demicube graphs with the hypercube graphs for fun here: User:Tomruen/demihypercube graphs, fun to see the projected vertices match but up a dimension for the demicube! Tom Ruen (talk) 01:13, 27 August 2008 (UTC)

A last (semiregular polytope) addition if you could figure them out, the two other En branches: Petrie_polygon#The_semiregular_E-polytope_family. I have some test element tables here: User:Tomruen/1_n2_E-polytope_family, User:Tomruen/2_n1_E-polytope_family.

If found, they could be named:

• File:Gosset 1 22 ortho petrie.svg, File:Gosset 1 32 ortho petrie.svg File:Gosset 1 42 ortho petrie.svg
• File:Gosset 2 31 ortho petrie.svg File:Gosset 2 41 ortho petrie.svg

Tom Ruen (talk) 01:23, 27 August 2008 (UTC)

I don't know how to get the vertices of these polytopes! I found a set of vertices for 1_32 (see talk), but my software for finding projection fails: I don't know if these coordinates are incorrect or if my software is incorrect. Do You have the coordinates or some reference to compute it? Rocchini (talk) 13:15, 5 September 2008 (UTC)

Thanks for trying! I have a graph of 1_22 from one of Coxeter's books, and vertex, edge counts, but not much else. I'll see what more I can find. Tom Ruen (talk) 16:21, 5 September 2008 (UTC)

I rewrote my search code using least square fitting and more vertices: I found a projection of Gosset 1 22 polytope, the vertex code is (12,24,12,24). Rocchini (talk) 11:42, 8 September 2008 (UTC)

Great job! Beautiful! :) 16:45, 8 September 2008 (UTC)

Math notation conventions

Please.

Look at Wikipedia:Manual of Style (mathematics) and at this edit.

• One should not promiscuously italicize everyting in non-TeX mathematical notation. Variables should be italicized, digits and parentheses should not.
• One should add a space before and after "+", "=", etc. I prefer to make these spaces non-breakable except sometimes with "=".
• A proper minus sign rather than a hyphen should be used. Thus:

5 − 3,

not

5-3.

• It is uncouth to use an asterisk for ordinary multiplication. That practice is for character sets in which it is impossible to write something like 3 × 5. (And in the case of the edit linked to above, simple juxtaposition seems more apt.)

I also don't understand the meaning of x and I in the case of the equation involved in this edit. Can those be explained in the caption? Michael Hardy (talk) 18:58, 30 August 2008 (UTC)

Sorry for very bad caption style. I try to write some more information: the i (now lowercase) represents ${\sqrt {-1}}$, and x the polynomial variable. If you want, add even more info. Rocchini (talk) 08:43, 3 September 2008 (UTC)

Conic sections

Hello Rocchini!

I was wondering if you might be interested in doing some diagrams for the conic sections article, similar to you Viviani's curve picture? If you're too busy, it's no problem of course. Cheers, Ben (talk) 18:23, 8 September 2008 (UTC)

The images of articles are good enough! Rocchini (talk) 08:34, 10 September 2008 (UTC)

Any software for mathematical diagrams?

Hi i'm a curious math fan and also enjoy drawing mathematical diagrams... can you suggest any software where i can draw diagrams (especially multidimensional figures)? Sorry for littering in your discussion page!Leif edling (talk) 07:39, 14 September 2008 (UTC)

I am sorry: for my drawings I write my software by myself directly in C++ (i.e. see or ). Fo some images I write a C++ routine for generating Povray scripts, or for very simple images I use Inkscape for hand-made drawings. Rocchini (talk) 17:13, 14 September 2008 (UTC)

E8 graph.svg file deletion

I think you need to take a look and help Melesse with this important image that has been deleted. +Image:E8_graph.svg

BTW - I love the graphs you guys User:Tomruen are doing. If you haven't already, you may want to check out my Mathematica based 8D to 2D/3D projection stuff. E8Flyer Jgmoxness (talk) 18:09, 5 October 2008 (UTC)

Thanks Jgmoxness. I uploaded a new copy, but I couldn't see WHY it was deleted! Tom Ruen (talk) 19:16, 5 October 2008 (UTC)

Snub 24-cell images

Hi Rocchini! I saw your recent edits to snub 24-cell and uniform polychoron, and I'm curious as to why you think your images are wrong. The new images I added to snub 24-cell are perspective projections at a distance, and so will appear differently from Schlegel diagrams and other perspective-type projections where the viewpoint is taken to be on the surface of the polytope. I think it would be nice to show both kinds of images, as they both offer different insights into the object.—Tetracube (talk) 15:34, 10 October 2008 (UTC)

My doubts are antecedents to these images. I am not sure that my code generates correct vertex position. I take some time to recheck the code, then I calculate a new version of the images. Rocchini (talk) 07:15, 13 October 2008 (UTC)

I appreciate your care. Thanks! Tom Ruen (talk) 16:11, 13 October 2008 (UTC)

If you want, I can send you the vertices of the snub 24-cell and the grand antiprism. I have them in ~20 digits precision.—Tetracube (talk) 02:45, 14 October 2008 (UTC)

Yes! Many thanks. Rocchini (talk) 07:21, 14 October 2008 (UTC)

Omnitruncated hexateron

Hi Rocchini! How difficult would it be to draw text with the projected omnitruncated hexateron with its 720 permutation coordinates of (1,2,3,4,5,6) as a permutohedron in 6-space? Image:Omnitruncated Hexateron.png. I know it'd be messy unles text very small, but maybe that would satisfy User:David_Eppstein?

ACTUALLY, the same is needed for the omnitruncated 5-cell, an image like Image:Omnitruncated 5-cell.png without solid faces, and labeled like Image:Permutohedron.svg. Tom Ruen (talk) 22:19, 14 October 2008 (UTC)

I try Image:Omnitruncated Hexateron as Permutohedron.svg and Image:Omnitruncated 5Cell as Permutohedron.svg. Rocchini (talk) 10:25, 16 October 2008 (UTC)

Very good attempt! Thanks! It is messy as I feared, but better than I hoped! We'll see what User:David_Eppstein says. (A small note, should index from 1,2,3, rather than starting from zero, but a trivial change.) Tom Ruen (talk) 17:51, 16 October 2008 (UTC)

Perhaps if you wanted to remake the image (especially the simpler order-5), try a truncated-octahedral-centered perspective projection into 3D first, and maybe with "cylinder edges" to get some 3D depth? Again, maybe best to see what David Eppstein says too.... Thanks! Tom Ruen (talk) 17:59, 16 October 2008 (UTC)

Klein bottle

Hey there. The article Klein bottle really needs a picture representing the two Mobius band decomposition. We need something like [7]. GeometryGirl (talk) 18:01, 31 October 2008 (UTC)

Hyperbolic honeycomb images

Hi Rocchini,

If you'd like to play with some uniform honeycombs again, I've enumerated a list of 76 uniform hyperbolic honeycombs with Coxeter-Dynkin diagrams and vertex figures:

Convex_uniform_honeycomb#Hyperbolic_forms

Currently we only show graphs of 3 regular ones:

Order-4_dodecahedral_honeycomb

Order-5_cubic_honeycomb

Order-3_icosahedral_honeycomb

Missing one regular:

Order-5_dodecahedral_honeycomb

I can't render any of these at all for now. If need to start somewhere, I'd most like to see the [5,3,4] family completed: Convex_uniform_honeycomb#.5B5.2C3.2C4.5D_family

But anything you can do to help is appreciated! :)

Tom Ruen (talk) 00:36, 3 January 2009 (UTC)

Hypergraph

Hi Rocchini - great praise! Shouldn't this hypergraph have one edge that links only to another edge, not to a vertex? Thanks. —Preceding unsigned comment added by 161.185.150.82 (talk) 16:13, 4 May 2010 (UTC)

Hi Rocchini, what did you use to draw  ?. I need a similar picture for my master thesis.

thanks

Cosenal (talk) 15:27, 28 January 2009 (UTC)

Hi,

I saw your images of the hyperbolic plane tilings. Maybe this is something you should know:

http://raoul.koalatux.ch/sites/hyperbolic_geometry/hyperbolic_geometry.html
http://raoul.koalatux.ch/sites/hyperbolic_geometry/hyperbolic_demos.html
http://raoul.koalatux.ch/sites/hyperbolic_geometry/hyperbolic_constructions.html —Preceding unsigned comment added by 83.76.114.187 (talk) 00:06, 22 December 2009 (UTC)

Uniform polytera/5-polytopes

Hi Rocchini! What a nice Christmas star you made at Stericated hexateron! Very nice!

I linked a "graph" column in the uniform polyteron tables if you'd like to try any others that don't have articles created (like #28, stericated penteract/pentacross?). I'll get around to finish sketching all the vertex figures for the uniform 5-polytopes/4-honeycombs, currently list at:User:Tomruen/Uniform_polyteron_verf. Tom Ruen (talk) 02:38, 24 December 2009 (UTC)

vertex neighborhoods

For each uniform polychoron it might help to show a vertex-centred orthographic projection of only those cells incident on that vertex (in skeletal form). What do you think? —Tamfang (talk) 20:37, 16 February 2010 (UTC)

Barnstars

		The Graphic Designer's Barnstar
		Your graphic work is extraordinary – undying thanks for your beautiful and tireless efforts. —Nils von Barth (nbarth) (talk) 06:01, 26 February 2010 (UTC)

		The E=mc² Barnstar
		A special thank you for File:Dunce hat animated.gif – as a math teacher I explained this to my students (who were tempted to sew one for me, but that’s neither here nor there), and of course could show them no more at the chalk board than the schematic – and now we have your wonderful animation, for future generations. Thank you. —Nils von Barth (nbarth) (talk) 06:01, 26 February 2010 (UTC)

How to do the impossible

Ciao Claudio,

I notice that you have some impossible missions. Since those are my favorite kind, I thought I’d share some ideas for them below – enjoy!

(I trust I’m not taking any of the fun out of this; this is just the math – the artistic problems…well, let’s just say that I mostly stick to commutative diagrams and graphs.)

—Nils von Barth (nbarth) (talk) 07:05, 26 February 2010 (UTC)

Prewellordering

Further information: Prewellordering

This seems easiest – just draw a Hasse diagram of a finite prewellordering (PWO), and the wellordering (WO) it yields underneath, as a quotient. Concretely, how about:

   1a  2a
0  1b  2b

0  1   2

(so 0 < 1a ~ 1b < 2a ~ 2b)? …with blue lines for the (6) left-right lines, and red lines for the (2) up-down lines.

You might also give counterexamples, like:

  a
0 b c

…where a and b are not comparable – and you could note that it admits 3 distinct PWO structures, corresponding to

  a
0 b c

0 a b c

0 b a c

(each total), but that’s perhaps overkill.

Rado graph

Further information: Rado graph

This has a pretty graph, File:Rado graph.svg, but presumably you mean that the existing graph is not very informative. The key ways to make a more informative graph are:

• arrange vertices on a cube, with the binary expansions, to make the binary clear
• only show the edges from one vertex at a time, to avoid overwhelming the viewer

E.g., have an animation, showing each frame, then conclude with showing all edges (optionally colored according to the lower vertex), then cycle, so “from 0, from 1, from 2, all”.

• distinguish between upward pointing and downward pointing edges (i.e., x < y and x > y) when drawing “edges from a given vertex”

E.g., color upward edges blue, downward red.

If you do this for the 2x2x2 (x,y,z) cube of 0,…,7, the upward pointing edges are very clear – they join 0 to the 0th far face (x=1), 1 to the 1st far face (y=1), 2 to the 2nd far face (z=2), and 3 to no faces – the geometry is clear, and the magic is in the vertex numbering.

Penteractic honeycomb

Further information: Penteractic honeycomb

Ok, this is just a problem of showing 5 dimensions in 3 – conceptually it’s easy.

The two key ways I know of fitting more dimensions down – which you probably know of / have probably thought of – are:

• map one dimension to an offset – e.g., a 3D chess board in 2D is easy: just show 3 chess boards! (just as we do for usual show of the cube and 4-cube)
• add time/make a video (the “Flatland” solution)

…and a graphical trick is:

• map one dimension to some added graphical feature, especially color – in this case, make distance in the 5th dimension correspond to fading

Looking at Tesseractic honeycomb, I’d say that a 2⁵ sample with alternating colors would work – draw the 2⁴ 4D honeycomb (4 tesseracts), then a faded copy next to it (say, on the right), with suitable connections (connections fade between bright and faded one).

Fancier would be to have a video showing movement in 5 dimensions: up/down, left/right, forward/back, in/out (in the tesseract (4th) dimension) – in these cases the two 2⁴ ones will move in sync, and then to move in the 5th dimension, you move the faded copy from right to left, it brightening as it moves, the existing one disappearing and a new faded copy coming into view from the right.

Obviously one can continue this trick in 6, 7, and more dimensions (having copies behind, above, then repeating), but it gets increasingly messy and busy.

Demipenteractic honeycomb

Are you kidding me? I have no idea. This is left as an exercise to the reader.

You could try your 5D-to-2D multiple projection method at File:Penteract projected.png. (Schlegel diagram from 5D to 4D, stereographic projection from 4D to 3D, and finally perspective projection from 3D to 2D.) Double sharp (talk) 11:39, 14 August 2012 (UTC)

A Schlegel diagram for an infinite object? I guess an inversion about the center of a cell could be so described. —Tamfang (talk) 03:14, 18 August 2012 (UTC)

Dyadic Transformation More Info?

Hi Rocchini - great work. I was trying to recreate the image of the Dyadic Transformation under Chaos and could use some help understanding the plot a little better. Do you have a high level algorithm you could post or send me or could I send you my description of what I think it is supposed to be? Thanks either way. Cunnagin (talk) 21:08, 9 June 2010 (UTC)

Here is my take on how your graph was created - I get something that 'hints' of your image, but is a ways off... I need HELP!

• (1) each point is a greyscale value (0-255); the horizontal axis is the 'x' axis (rational numbers from 0-1) and the vertical axis is the 'y' axis (real numbers from 0-1)
• (2) i choose a bunch of random initial points for x0
• (3) for each point x0 in the above set, i create the iterated sequence x1, x2, x3...xn using the dyadic transformation: y=f(x)=2*x mod 1
  • (a) at each step of iteration I index my graph at position <x,y> where x=x0 (the initial point) and y={x1, x2, ... xn}; so, 'n' coordinate pairs
  • (b) at each coordinate pair, I store some greyscale value; i am choosing to map 'n' to the range (0-255) so at <x0,x1> i store a value of 1, at <x0,x2> i store a value of 2, etc...

Cunnagin (talk) 19:34, 10 June 2010 (UTC)

I have added C++ source code on the image page. Some notes; the rational arithmetic is exact; I set a pixel in real position; the start x0 is not random

but fix, heach iteration stop on the first loop. Rocchini (talk) 12:45, 11 June 2010 (UTC)

Rock-n-Roll! Thanks so much - it makes sense now how you're aliasing the greyscale from the real fractional position. Keep up the good work and thanks for getting back to me so quickly! 192.146.101.71 (talk) 14:01, 11 June 2010 (UTC)

Graphe style

Hello

As you can see on Gallery of named graphs, I have changed the style of my graphs (no more red vertices). This is mainly for avoiding copyvio issues with MathWorld on some classical drawing.

I have also edited a few graphs drawn by David Eppstein for changing red vertices to blue vertices. Can I change the style of your graphs when required ? A good example would be File:Gewirtz_graph_embeddings.svg (on this example, colours don't provide any informations). Koko90 (talk) 13:44, 20 July 2010 (UTC)

Yes, of course. Thanks for your work. For my next works, I will try to follow your style. Rocchini (talk)

Schläfli graph

Hello, I'm studying the Schläfli graph at my engineering school in France and I would like to know if you have a javascript code to give please because I can't find it on internet. Thank you,

Angeline Besland (talk) 11:16, 20 January 2013 (UTC)

Code making what? The original page [sgraph] - section Code, gives the C++ code (not javascript) making the graph structure. The symmetric embedding is done using Nauty. For a complete example of Nauty code, you may consult [mclaughlin graph] section code. Rocchini (talk) 12:27, 21 January 2013 (UTC)

Copyrights for Enneract

Rocchini- I sent you an email about copyrights for the enneract. Please have a look!

Thanks!

Romanmgl (talk) 21:47, 22 August 2010 (UTC)

Hi Romanmgl. I originally asked Rocchini to make the Coxeter-plane hypercube graphs, including the enneract/9-cube, and subsequently made better ones, with vertices colored by overlap order. As far as I've seen no one else has made these graphs, although I got the idea originally from some of Mathworld's polytope graphs. Tom Ruen (talk) 01:40, 24 August 2010 (UTC)

File:Kochanek bartels spline.svg

Kochanek bartels spline

Regarding image File:Kochanek bartels spline.svg, there seems to be something wrong with the scale at the top of the image. See Wikimedia commons file talk page here. Are you able to check and, if necessary, change the file? Happy editing. Gaius Cornelius (talk) 17:29, 5 November 2010 (UTC)

Nomination of Sacks spiral for deletion

A discussion has begun about whether the article Sacks spiral, which you created or to which you contributed, should be deleted. While contributions are welcome, an article may be deleted if it is inconsistent with Wikipedia policies and guidelines for inclusion, explained in the deletion policy.

The article will be discussed at Wikipedia:Articles for deletion/Sacks spiral until a consensus is reached, and you are welcome to contribute to the discussion.

You may edit the article during the discussion, including to address concerns raised in the discussion. However, do not remove the article-for-deletion template from the top of the article.

You added a very nice graphic to this article a few years ago. Unfortunately, the article itself appears to be a vehicle for promoting somebody's original research. I thought I should let you know. (It's possible there's more to the story than I have been able to find.) Will Orrick (talk) 16:54, 7 November 2010 (UTC)

Thanks for your mathematical illustrations!

		The E=mc² Barnstar
		For your latest batch of illustrations to mathematics articles. —David Eppstein (talk) 18:01, 25 May 2012 (UTC)

Kautz graph

Hi Rocchini,

Your picture for the Kautz graph is wrong. Each node on the graph on the right should have 2 arrows pointing to it and 2 arrows exiting it. See for example http://ars.els-cdn.com/content/image/1-s2.0-S0166218X03004633-gr1.jpg on the left, that one is correct.

Best, --MathsPoetry (talk) 19:57, 23 December 2012 (UTC)

Thank you very much for this alert! You have given me the opportunity to redraw the image in svg format (without a push I would not have done this). Rocchini (talk) 09:10, 2 January 2013 (UTC)

You're welcome. And happy new year (e tanti auguri). --MathsPoetry (talk) 13:52, 3 January 2013 (UTC)

It's fixed in every language now (including Farsi), and the old image has been deleted from Commons today. Affair closed! --MathsPoetry (talk) 17:59, 9 January 2013 (UTC)

I had also tried to change the farsi, but did not succeed. Rocchini (talk) 07:16, 10 January 2013 (UTC)

Yes, mixed handwriting direction can make one nuts. I only succeeded with a help of a Farsi contributor. --MathsPoetry (talk) 15:36, 11 January 2013 (UTC)

http://upload.wikimedia.org/wikipedia/commons/c/c2/Involute_wheel.gif

Hi Rocchini,

great picture. Congratulations! Although there is one mistake: The addendum diameter of one gear wheel is touching the root diameter of the other gear wheel and vice versa. There must be a gap between the gears meshing with each other.

Could you please change that?

Thanks a lot. 93.133.187.30 (talk) 06:06, 9 February 2013 (UTC)

Thanks for this note, but I have lost the image source project so I can not regenerate It. Rocchini (talk) 13:17, 11 February 2013 (UTC)

Hyperbolic tilings

Hi. Uniform tilings in hyperbolic plane has expanded greatly recently to include a lot more symmetry groups. A while ago you created some very nice dual images for *732, *542, and *433. If you're not too busy at the moment, could you make some more pictures to fill up the gaps that Tomruen and I haven't filled up yet? Double sharp (talk) 14:03, 11 February 2013 (UTC)

No hurry Rocchini, but you do a great job! And I don't know if Rocchini could automate batches of tilings, but it's mostly the uniform duals, and color decision is undefined. My current ideal for coloring is single-color by default, and alternate coloring if all vertex orders are even (cases where they represent a set of intersecting mirror lines of fundamental domains.) Tom Ruen (talk) 19:27, 11 February 2013 (UTC)

Hyperbolic honeycombs

Hi Rocchini,

Sometime, if you have some spare time and want a challenge, it would be great to have some images like at Order-5 cubic honeycomb or Icosahedral honeycomb, for paracompact families which include Euclidean facets, including 11 regular honeycombs: {6,3,3}, {3,3,6}, {4,4,3}, {3,4,4}, {6,3,4}, {4,3,6}, {6,3,5}, {5,3,6}, {4,4,4}, {3,6,3}, and {6,3,6}. At least ONE picture of one of these would give a little more reality to these objects, and they are fully renderable as 3D. If you drew one transparent cell/facet, some facets would be infinite tilings, like {6,3,3} has regular facets {6,3}, while {3,3,6} would have tetrahedral facets, {3,3}, but an infinite vertex figure {3,6}. Anyway, at your convenient, they're enumerated at paracompact uniform honeycombs. (The finite subgroup (compact) hyperbolic honeycombs are at Uniform_honeycombs_in_hyperbolic_space which include two of your old pictures of {4,3,5} and {3,5,3}). Thanks! Tom Ruen (talk) 01:15, 12 June 2013 (UTC)

Hi, great Tom! I'm traveling for two months: I work on when I get back. Rocchini (talk) 11:55, 16 June 2013 (UTC).

Thanks for considering. Your images are always wonderful. Have fun! Tom Ruen (talk) 23:20, 16 June 2013 (UTC)

Here are some initial images. I have rewritten the code from scratch: now I generate the geometry using our Coxeter–Dynkin diagram. For now the code crash in almost all cases (always with two active nodes ...). I move the camera from outsize the sphere to the center (like our posted image): the structure is much more readable. By.

Rocchini (talk) 08:25, 9 August 2013 (UTC)

Thanks so much Rocchini! Very exciting progress! I like the central projection better to see the local structure. Thanks for adding some compact and paracompact examples. I'd be glad if you could automate generation, but no hurry. This is GREAT! Tom Ruen (talk) 08:33, 9 August 2013 (UTC)

Hi Rocchini! Looking further File:Hyperbolic_3d_order_6_tetrahedral.png disturbs me as {3,3,6}. It's hard to "see"(!!!), but in {3,3,6} there ought to be infinite vertex figures {3,6}, i.e. all the vertices perhaps are ideal, very similar to this 2D tiling Infinite-order triangular tiling, {3,∞}, (vertices all on the surface of the projective sphere). But I'm not sure what your honeycomb is showing. This is all great, and at least with 3D there's enough visual feedback to see if there are problems. I'm sorry I can't offer any more help, when you have some time to look again. Thanks again! Tom Ruen (talk) 00:46, 19 August 2013 (UTC)

Damn! I made ​​a mess: this is Rectified order-6 tetrahedral not Order-6 tetrahedral (you see twelve edges out of each vertex, i.e. the vertex figure is the Hexagonal prism). Rocchini (talk) 07:38, 20 August 2013 (UTC)

Thanks for figuring this out. I made a rename request at File:Hyperbolic 3d order 6 tetrahedral.png Tom Ruen (talk) 00:19, 21 August 2013 (UTC)

p.s. On the (4+11) regulars, perhaps you can try consistent "inside" and Poincare views of the first 4 compacts, and 4 paracompact with finite verfs. I'm just thinking the 7 with all ideal vertices might be the tougher ones? Tom Ruen (talk) 04:03, 21 August 2013 (UTC)

• Compact:

  Good: {5,3,5}

  Needed: {3,5,3}, {4,3,5}, {5,3,4}

• Finite Vertex figure paracompact:

  Good: {6,3,3}, {6,3,4}

  Needed: {4,4,3}, {6,3,5}

• Ideal vertex paracompact:

  Tough? {3,3,6}, {3,4,4}, {3,6,3}, {4,3,6}, {4,4,4}, {5,3,6}, {6,3,6}.

There are lots of pretty relational sequences we can show with your pictures, like this pure hyperbolic sequence: {6,3,p}

{6,3,p} honeycombs
Space	H3
Form	Paracompact				Noncompact
Name	{6,3,3}	{6,3,4}	{6,3,5}	{6,3,6}	{6,3,7}	{6,3,8}	... {6,3,∞}
Coxeter
Image
Vertex figure {3,p}	{3,3}	{3,4}	{3,5}	{3,6}	{3,7}	{3,8}	{3,∞}

Hi Rocchini, whenever you have time to try more, there is ONE important and easy regular paracompact honeycomb: {4,4,3} should work just like the beautiful {6,3,3}, but square tilings instead of hexagonal tilings. Maybe we could play a crazy hyperbolic chess game there? Tom Ruen (talk) 04:07, 9 November 2013 (UTC)

Hi Rocchini. Today I saw a video with 3D printer models of hyperbolic honeycombs, including {6,3,3}! [8] Tom Ruen (talk) 23:13, 10 December 2013 (UTC)

p.s. All the regulars done as of December by commons:User:Roice3. Tom Ruen (talk) 22:50, 8 February 2014 (UTC)

Can you tell me something about your tools and techniques? I would love to make the complete series of 227. —Tamfang (talk) 21:19, 8 February 2014 (UTC)

Kochanek Bartels Spline Diagram

Hi Rocchini,

I noticed that the Kochanek Spline Diagram you made has a small numerical error in it. It's 3rd column is labelled as 1.5 rather than 0.5. http://en.wikipedia.org/wiki/File:Kochanek_bartels_spline.svg

Thanks, file corrected. Rocchini (talk) 13:32, 8 August 2013 (UTC)

Una barnstar per te!

	La barnstar del progettista grafico
	Bellissimi i tuoi lavori - Mi affascinano Assianir (talk) 14:46, 8 August 2013 (UTC)

Good day -- Kaleidoscope Algorithm under petrie polygon orthogonal hypercube vector multiplier PX and PY

https://commons.wikimedia.org/wiki/File:600-cell_petrie_polygon.svg?uselang=fr?uselang=fr

I am attempting to uncover how the origin of the "magical" values midst aforlinked orthographic hypercube, petrie polygon graph.

If you control find (ctrl+f) "// Magics! Hard to find projection directions" You shall observe the values to which I am referring.

I see that you are quite familiar with measure polytopes (5d orthographically produced hypercubes).

How do you compute these "magic values"?

What do I Know?

Perhaps, I envision that the aforsaid "magic" values manifest as some form of vector multiplier, that directly relate with the petrie polygon's dimension cardinality.

Furthermore, I ascertain it is linked with Coxeter Dynkin approximations per petrie polygon, measure polytope. (As you have stated this)

In exemplification, I have noticed that per orthogonalized hypercube of n dimensions, each PX and PY array, contains a periodic sequence of exactly n directional projection vector multipliers.

As to how such multipliers are achieved, I am uncertain.

I would like to include this in an artificial intelligence I am developing.

I WOULD ESPECIALLY DESIRE LEARNING HOW YOU COMPUTE THE VERTEX MULTIPLIERS PER PX, PY ARRAY, IN MEASURE POLYTOPES SUCH AS OCTERACTS. I have observed some general rules, albeit I AM UNABLE to compute these vertex multipliers.

Are these multipliers perhaps directly related to DEGREES OF FUNDAMENTAL IN-VARIANCE, under coxeter groups par polytopes?

Thanks. — Preceding unsigned comment added by JordanMicahBennett (talk • contribs) 02:38, 10 July 2014 (UTC)

Hello Jordan, I'm unsure if Rocchini will answer, but I've done the calculation for hypercubes, basically solving a system of equations that map a sequence of points in N-Dimensions into a regular polygon on the unit circle of points in 2D. In the end you just get two orthogonal vectors [u,v] in nD which represent the plane of projection. The hypercube solution vectors are copied here. Tom Ruen (talk) 05:50, 10 July 2014 (UTC)

[Here] the complete source code of projection calculation Rocchini (talk) 06:07, 10 July 2014 (UTC)

Jordan, this may be what you are looking for:

It is the logic (in Mathematica) for generating the numeric values Tom referenced

(as well as the projections for the 120 and 600 cells that Rocchini used for his "Magic" (as well as mine).

You will have to translate to c++ or any other syntax, but...

Jgmoxness (talk) 14:20, 10 July 2014 (UTC)

BTW - the numbers will vary by a scaling factor (I use 1/2), but the salient point is the Sin or Cos of an iterator divided by the desired nCube. This code also appends an array of zeros to project from a larger dimensional structure (e.g. from E8 which contains the nCubes from 1-7).

You also might find it interesting that you can "fold" the 240 vertices of the E8 to the 120 vertices of the 600 Cell=H4 (plus 120 more vertices of H4/phi) by taking each E8 vertex (e.g. of the split real even E8 group) and applying a dot product with the following matrix:

I believe I am the only one to discover this fact...(see [[9]])

Bottom line is that from a folded E8 you get the H4 (600 cell directly related to the 120 cell) and then with a simple dot product generate the 2D or 3D projections you desire.

Jgmoxness (talk) 01:41, 11 July 2014 (UTC)

Beknownst you all, my thanks are non liminal. Jgmoxness, I am not astonished that backwards computability insurges midst 600, and 120 cellular orthogonalized structures.

As a matter of factum, 2 days ago (when I initially stumbled in petrie polygons), I observed that if we take the edge cardinality aligned with dimension d, and divide it by said dimension, we obtain the vertex total for previous dimension. //eg. d=7, e=192, [V] under d-1 = e/d = 32, which is correct.

This simple ruling revealed backwards implication therein.

I have in the like, observed this instance amidst many a life instance. In exemplification, after I formulated an equation in consciousness, it may be easily observed that every entity midst this verse tends to a particular singularity midst the space of time.

consciousness equation>>

(see [[10]])

as such, computing this equation yields this facing factum: (see [[11]]) — Preceding unsigned comment added by JordanMicahBennett (talk • contribs) 02:20, 12 July 2014 (UTC)

I thank you all :) — Preceding unsigned comment added by JordanMicahBennett (talk • contribs) 02:16, 12 July 2014 (UTC)

Spieker circle diagram

FYI, the diagram for Spieker circle has one misplaced cleaver. It should not be at a right angle to the medial triangle's edge, but run through a vertex and its incentre.

Thanks for reporting. I corrected the diagram , I also added an example of measurement and the source code. Rocchini (talk)

File:Dykstra algorithm.svg

Hi. Thx for new image. What is Carmetal project ? --Adam majewski (talk) 16:18, 2 August 2015 (UTC)

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is there something wrong with Poincare halfplane eptagonal hb

I was wondering about the file File:Poincare halfplane eptagonal hb https://en.wikipedia.org/wiki/File:Poincare_halfplane_eptagonal_hb.svg and I think it is wrong.

As far as I understand it hyperbolic straight segments in the Poincaré half-plane model should be parts of circle arcs of circles that are orthogonal to the x axis. (or in rare cases a segment orthogonal to the x axis)

But in this file the main lines (the black ones) are parts of straight lines and thus no sepments at all. Can you correct this, or am i wrong? for the moment I have commented out the file at Poincaré half-plane model. WillemienH (talk) 22:05, 19 April 2016 (UTC)

The black lines do not appear to me to be straight, but I am not sure whether they are curved as much as they should be. JRSpriggs (talk) 05:08, 20 April 2016 (UTC)

If you look carefully, you will see the main black lines are parts of circle arcs orthogonal to the x axis, not a straight segment Rocchini (talk)

Thanks, somebody else allready reinstated it , sorry for being doubtful. WillemienH (talk) 08:21, 21 April 2016 (UTC)

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Hypercycle illustration

Hello, Rocchini.

You have made a very nice illustration of a hypercycle: https://en.wikipedia.org/wiki/Hypercycle_(geometry)#/media/File:Hypercycle_(vector_format).svg .

However, in the picture there are two red curves, only one of which is described in the caption.

I suspect that the other red curve is the equidistant curve to the given geodesic that is on the other side of that geodesic. Is that correct?

Whatever the case may be, I suggest that this other red curve be explained in the caption. Certainly, you are the best person to do this. 2601:200:C000:1A0:6CE8:4EF:EF18:56C0 (talk) 23:32, 9 September 2021 (UTC)

Ops! This is actually my mistake: I misunderstood the definition of HC. I believed that HC was made up of all equidistant points. I corrected the design and also the source code. Thanks for the kind report! Rocchini (talk) 08:17, 11 September 2021 (UTC)

Just noticed that it looks great now! Thank you! 2601:200:C000:1A0:D028:9F22:534E:3701 (talk) 17:01, 13 September 2021 (UTC)

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A barnstar for you!

	The Original Barnstar
	What great work! I'm creating an archive for Hurricane Katrina and investigating self-orgainized criticality as part of my work. Your illustration of the Bak theory is wonderful. May I use it on my site with proper credit to you? Thanks so much. Pls excuse my lack of Italian language skills. Nola0829 (talk) 14:39, 8 January 2022 (UTC)