Polyhedra

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Edge-Transitive Polyhedra

Last post by Gordon « Tue Aug 27, 2024 4:18 am
Replies: 10
by Gordon » Sun Aug 28, 2022 2:20 am

One can find a lot of things written about face- and vertex-transitive polyhedra, especially regular-faced ones. There is not much on edge-transitive...

10 Replies

36289 Views

Last post by Gordon
Tue Aug 27, 2024 4:18 am
Near-Miss Johnson solids

Last post by Wagyx « Fri Aug 02, 2024 7:06 pm

by Wagyx » Fri Aug 02, 2024 7:06 pm

Hello there,

I have made a web page about near miss Johnson solids where I am collecting models made by people across the internet.
The models are...

0 Replies

1990 Views

Last post by Wagyx
Fri Aug 02, 2024 7:06 pm
Geometric construction of Truncated Cuboctahedron Polytope

Last post by robertw « Fri Feb 23, 2024 1:40 pm
Replies: 12
by asherwin » Wed Sep 20, 2023 4:05 am

Hi,

I recently got really into geometrically constructing polytopes in GeoGebra (probably not the best software to use) such as the 120-cell (or...

12 Replies

55669 Views

Last post by robertw
Fri Feb 23, 2024 1:40 pm
icosahedron construction

Last post by Ulrich « Tue Dec 05, 2023 5:54 pm
Replies: 4
by jacpot » Mon Dec 04, 2023 4:55 pm

Hello everyone,
my questions are in the photo,
Sincerely

4 Replies

35766 Views

Last post by Ulrich
Tue Dec 05, 2023 5:54 pm
the 59 stellations of the icosahedron

Last post by jacpot « Sun Dec 03, 2023 2:46 pm
Replies: 2
by jacpot » Sun Dec 03, 2023 9:45 am

Hello everyone,
I am starting to manufacture the 59 stellations of the icosahedron.
I notice inconsistencies in the numbering of the stellations,...

2 Replies

13762 Views

Last post by jacpot
Sun Dec 03, 2023 2:46 pm
Golden Rhombic Polyhedron made from Dodecahedra

Last post by Wagyx « Sat Aug 26, 2023 3:02 pm

by Wagyx » Sat Aug 26, 2023 3:02 pm

Hello there,

I have been playing with dodecahedra and found in the Stella database two Stewart's solids made only with dodecahedra:
a ring of 8...

0 Replies

30485 Views

Last post by Wagyx
Sat Aug 26, 2023 3:02 pm
Miller's Monster

Last post by robertw « Fri Jan 06, 2023 2:30 pm
Replies: 16
by oxenholme » Wed Dec 09, 2009 12:57 pm
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2
I made it out of white cartridge paper back in the 60s.

I'm thinking of making it again, but this time in colour. Presumably six colours for the...
16 Replies

70402 Views

Last post by robertw
Fri Jan 06, 2023 2:30 pm
How hard would it be to compute true filling?

Last post by guy « Mon May 02, 2022 11:53 am
Replies: 8
by metachirality » Mon Dec 23, 2019 11:09 pm

True filling is filling regions of a polytope if they can be continuously transformed into a region of odd density. How feasible is this in practice?

8 Replies

31642 Views

Last post by guy
Mon May 02, 2022 11:53 am
Possible Wenninger Erratum

Last post by guy « Sun May 01, 2022 4:40 pm
Replies: 3
by TomF » Fri Jan 14, 2022 9:27 pm

I just completed a model of the great icosahedron using the directions in Polyhedron Models. There appears to be a mistake in line (2) of the color...

3 Replies

19220 Views

Last post by guy
Sun May 01, 2022 4:40 pm
Need images of platonician polyhedra inside one another

Last post by robertw « Fri Dec 24, 2021 6:54 am
Replies: 3
by Carabama » Thu Dec 23, 2021 11:31 am

Hello to all,
I need specific images of platonician polyhedra inside one another. I am ready to pay for the work so please get in touch if you are...

3 Replies

18067 Views

Last post by robertw
Fri Dec 24, 2021 6:54 am
What is this Polyhedra called.

Last post by eligius1427 « Sun Oct 31, 2021 3:33 pm
Replies: 7
by eligius1427 » Sun Oct 17, 2021 10:15 pm

Hello, I found this toy and am curious what geometric form it is called. It is essentially 6 5-pointed stars interwoven. At first I thought it was a...

7 Replies

23819 Views

Last post by eligius1427
Sun Oct 31, 2021 3:33 pm
Two new noble polyhedra - a new source of convex hulls to search from?

Last post by Ulrich « Thu Sep 30, 2021 7:53 am
Replies: 27
by senkoquartz » Fri Oct 09, 2020 6:10 am
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2
.stel and .off file

By taking uniform polyhedron duals, and isohedrally faceting them, and then taking the duals of those, you get isogonal...
27 Replies

74850 Views

Last post by Ulrich
Thu Sep 30, 2021 7:53 am
Sharpohedron

Last post by marcelteun « Thu Apr 01, 2021 5:31 pm
Replies: 18
by marcelteun » Wed Mar 10, 2021 10:54 am
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2
Hi

Some time ago George Hart posted a polyhedron on Instagram and some time late, since he got some questions, he made a little video, which can be...
18 Replies

58204 Views

Last post by marcelteun
Thu Apr 01, 2021 5:31 pm
New Uniform Polychora

Last post by robertw « Sun Jan 31, 2021 1:07 pm
Replies: 15
by Mecejide » Thu Oct 01, 2020 12:59 am
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2
Recently, two new uniform polychora were discovered by someone on the Higher Space Forum named “_Geometer”. They both have 360 tetrahedra, 240...
15 Replies

50694 Views

Last post by robertw
Sun Jan 31, 2021 1:07 pm
Heptagons

Last post by senkoquartz « Sat Oct 24, 2020 7:30 pm
Replies: 11
by marcelteun » Mon Sep 30, 2019 10:14 am

Some of you might know that I am interested in heptagons. The background for this interest is that if you ignore polyhedra with prism and anti-prism...

11 Replies

36001 Views

Last post by senkoquartz
Sat Oct 24, 2020 7:30 pm
What are your favorite polyhedra?

Last post by marcelteun « Mon Oct 05, 2020 1:48 pm
Replies: 5
by senkoquartz » Sat Sep 19, 2020 9:44 pm

My #1 is the octahedron (perfect)
Some of my favorites are the great rhombicuboctahedron and great deltoidal icositetrahedron (very deep and very...

5 Replies

23828 Views

Last post by marcelteun
Mon Oct 05, 2020 1:48 pm
A list of every* isohedral triacontahedron, plus every* rigidly isohedral polyhedron, and a list of nobles

Last post by senkoquartz « Mon Sep 28, 2020 6:02 am
Replies: 7
by senkoquartz » Fri Aug 21, 2020 11:42 pm

Microsoft OneDrive link to files:

If you go through Tidy Facetings and Duals of the icosidodecahedron, there are 4379 results, 3671 of which have...

7 Replies

26316 Views

Last post by senkoquartz
Mon Sep 28, 2020 6:02 am
Noble polyhedra. Where can I find them?

Last post by marcelteun « Mon Aug 17, 2020 8:49 am
Replies: 17
by senkoquartz » Wed May 20, 2020 2:01 pm
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2
I found out about noble polyhedra a few days ago. I was looking at the final icosahedron stellation and realized it's an isohedral isogonal figure...
17 Replies

51594 Views

Last post by marcelteun
Mon Aug 17, 2020 8:49 am
Polyhedral Chess Set

Last post by senkoquartz « Thu Aug 06, 2020 9:58 am
Replies: 5
by Nordehylop » Sun May 04, 2008 7:31 pm

I had the idea a while ago of building a chess set with the regular polyhedra as the pieces. Only one problem: six chess piece types, five regular...

5 Replies

42497 Views

Last post by senkoquartz
Thu Aug 06, 2020 9:58 am
Gilson: Polyhedra - A New Approach

Last post by kohli149 « Tue Jul 28, 2020 9:19 am
Replies: 20
by Peter Kane » Thu Sep 27, 2012 3:41 pm
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2
Noticed a new book on Amazon the other day, so dipped into my piggy bank. Its by Bruce R. Gilson and the new approach is to consider polyhedra from...
20 Replies

103325 Views

Last post by kohli149
Tue Jul 28, 2020 9:19 am
Puzzle: count the cubes!

Last post by robertw « Sat Apr 04, 2020 4:41 am

by robertw » Sat Apr 04, 2020 4:41 am

I put together a little puzzle, to count intersecting cubes. You can test your answers and I just added hints in the form of colours.

Let me...

0 Replies

41460 Views

Last post by robertw
Sat Apr 04, 2020 4:41 am
Cundy & Rollett

Last post by Peter Kane « Fri Mar 13, 2020 5:19 pm

by Peter Kane » Fri Mar 13, 2020 5:19 pm

I was browsing through some old posts in this section, when I came across a reference to Mathematical Models by Cundy & Rollet. A little later, I was...

0 Replies

41918 Views

Last post by Peter Kane
Fri Mar 13, 2020 5:19 pm
Super-holey faceting of icosahedron

Last post by metachirality « Sat Dec 21, 2019 12:04 am

by metachirality » Sat Dec 21, 2019 12:04 am

I found this polyhedron while going through facetings of the snub tetrahedron/icosahedron. Has anyone seen this before? I find this faceting to be...

0 Replies

41839 Views

Last post by metachirality
Sat Dec 21, 2019 12:04 am
Compounds of Cubes & Tetrahedra

Last post by marcelteun « Tue Oct 08, 2019 8:53 am
Replies: 8
by marcelteun » Thu Feb 14, 2008 1:48 pm

I understand that it is not straightforward to create compounds in Stella (I don't use Stella myself, yet). Therefore I thought that Stella users...

8 Replies

57677 Views

Last post by marcelteun
Tue Oct 08, 2019 8:53 am
Constructing models with transparent faces?

Last post by robertw « Wed Oct 02, 2019 7:18 am
Replies: 8
by robertw » Sat Sep 29, 2018 5:11 am

Has anyone built physical models with transparent faces? (Either some or all faces)

I'm thinking more of thin materials, like clear plastic, rather...

8 Replies

33941 Views

Last post by robertw
Wed Oct 02, 2019 7:18 am
Solved twisty puzzle

Last post by Ulrich « Mon Feb 11, 2019 5:25 pm
Replies: 5
by robertw » Sun Feb 10, 2019 3:49 am

After sitting scrambled on my shelf for years, I finally figured out how to solve this beautiful puzzle! Seen here sitting on the page of scribbles...

5 Replies

27674 Views

Last post by Ulrich
Mon Feb 11, 2019 5:25 pm
New Torus

Last post by ndl « Thu Dec 20, 2018 2:54 am
Replies: 9
by ndl » Thu Nov 29, 2018 3:31 am

I found a new interesting equal-edged torus today by excavating two J92's out of an icosidodecahedron

ID-J92 Torus.jpg

Has anyone ever made this...

9 Replies

36853 Views

Last post by ndl
Thu Dec 20, 2018 2:54 am
Constructing a shape as near to a sphere as possible

Last post by Peter Kane « Fri Sep 28, 2018 4:16 pm
Replies: 3
by Squeaky » Fri Nov 24, 2017 7:06 am

Hi,

I wish to construct a shape from different coloured hardwoods that is as near to a sphere as possible
I have a CNC machine
Any ideas

3 Replies

26642 Views

Last post by Peter Kane
Fri Sep 28, 2018 4:16 pm
Nadia's Icosahedron

Last post by Ulrich « Fri Sep 28, 2018 7:03 am
Replies: 13
by sicherman » Sat Sep 22, 2018 5:52 pm

Donald Bell has written up a polyhedron discovered by a young visitor to his home. He calls it Nadia's Icosahedron.

It has a girdle of six regular...

13 Replies

42088 Views

Last post by Ulrich
Fri Sep 28, 2018 7:03 am
What is a step prism?

Last post by robertw « Mon Aug 13, 2018 3:29 am
Replies: 3
by Nikayama NDos » Tue Aug 07, 2018 11:36 am

It's outstanding that all 4D dice with 5+ cells is possible, gyrochora being the general method.
Stella4D tells gyrochora are dual of step prisms,...

3 Replies

73121 Views

Last post by robertw
Mon Aug 13, 2018 3:29 am
Isohedral Stellations

Last post by ndl « Mon Feb 20, 2017 2:14 am
Replies: 4
by ndl » Wed Feb 15, 2017 5:17 am

I'm interested in finding all the convex isohedral stellations of various polyhedra. I found (including stellation core):
Dodecahedron: 4...

4 Replies

30566 Views

Last post by ndl
Mon Feb 20, 2017 2:14 am
Coloring of Snub Dodecahedron

Last post by Ulrich « Sun Oct 02, 2016 1:19 pm
Replies: 3
by the_tool_man » Fri Sep 23, 2016 4:40 pm

Hi all:
I've been using Great Stella for a few years now, slowly building a collection of polyhedra. I'm on the last of the Archimedean solids, the...

3 Replies

36350 Views

Last post by Ulrich
Sun Oct 02, 2016 1:19 pm
Archimedean polyhedra with missing faces

Last post by guy « Thu Aug 13, 2015 7:16 pm
Replies: 1
by Kagome » Thu Aug 13, 2015 3:57 pm

I am wondering if there might be someone out there who can help with a question I have.

If you take an Archimedean Polyhedron (say an...

1 Replies

30950 Views

Last post by guy
Thu Aug 13, 2015 7:16 pm
Compound of 3 Rhombic Prisms

Last post by jos smits « Sun Mar 08, 2015 7:59 am
Replies: 12
by jos smits » Fri Feb 27, 2015 12:07 pm

Robert Austin excited me with his model of a compound of 3 Rhombic Prisms made with Stella. I asked him how he made it but he answered that he had no...

12 Replies

66720 Views

Last post by jos smits
Sun Mar 08, 2015 7:59 am
Crossed heptagrammic cuploid

Last post by Evenire « Wed Jan 14, 2015 7:28 pm
Replies: 2
by Evenire » Mon Jan 12, 2015 2:16 pm

Hello guys!

Does this shape exist in Stella4D?

Cheers
Bob

2 Replies

28760 Views

Last post by Evenire
Wed Jan 14, 2015 7:28 pm
compound of 2 icosahedra

Last post by jos smits « Fri Oct 31, 2014 8:02 pm

by jos smits » Fri Oct 31, 2014 8:02 pm

Just bought Great Stella4D. Happy to join the club of symmetrists. Having built quite a few models over the past years I am ready to tackle the...

0 Replies

50352 Views

Last post by jos smits
Fri Oct 31, 2014 8:02 pm
Groupe Facebook

Last post by rgagneux « Sun Oct 06, 2013 12:59 pm
Replies: 6
by rgagneux » Wed Sep 18, 2013 7:06 pm

Bonjour,
Je vous rappelle qu'il existe un groupe Facebook où vous pouvez publier vos créations virtuelles, ou concrètes.

6 Replies

36013 Views

Last post by rgagneux
Sun Oct 06, 2013 12:59 pm
Rectified Polyhedra

Last post by robertw « Thu May 23, 2013 11:56 pm
Replies: 3
by Pauly1060 » Mon May 20, 2013 11:02 pm

I have great stella and would like to make rectified polyhedra from a parent polyhedron, twisting the pentagon faces of a dodecahedron for example,...

3 Replies

32871 Views

Last post by robertw
Thu May 23, 2013 11:56 pm
Faceted snub cube

Last post by Ulrich « Thu Mar 28, 2013 7:14 pm
Replies: 13
by robertw » Mon Feb 11, 2008 6:46 am

I just discovered an interesting little faceting of the snub cube. Has anyone seen it before?

It's interesting because it has just one face-type, an...

13 Replies

87322 Views

Last post by Ulrich
Thu Mar 28, 2013 7:14 pm
Procedure to make compounds

Last post by Kathy « Thu Jul 05, 2012 7:09 pm
Replies: 3
by Kathy » Tue Jul 03, 2012 12:35 am

Hi,
I am trying to make a compound but am unable to find the procedure. I have a faceted tetrahedra that I want to make into a compound 5. Thanks...

3 Replies

34729 Views

Last post by Kathy
Thu Jul 05, 2012 7:09 pm
Icosahedon 5 compound - anyone tried making one?

Last post by Peter Kane « Thu Mar 15, 2012 11:34 am
Replies: 7
by indigotwilight » Mon Jun 20, 2011 2:20 pm

I've just started building the compound of 5 dodecahedra, and thought it might be nice to make its dual, the compound of 5 icosahedra, as well. The...

7 Replies

44111 Views

Last post by Peter Kane
Thu Mar 15, 2012 11:34 am
Compound of Two Deltahedra

Last post by indigotwilight « Fri Apr 22, 2011 3:01 pm
Replies: 10
by oxenholme » Mon Aug 17, 2009 12:22 pm

Due to a never-ending tale of woe with broken computers I haven't got access to Stella at the moment...

You know the deltahedron - same edges as the...

10 Replies

61736 Views

Last post by indigotwilight
Fri Apr 22, 2011 3:01 pm
Do you ever make polyhedra for other people?

Last post by Peter Kane « Tue Mar 29, 2011 6:56 am
Replies: 7
by oxenholme » Sat Dec 26, 2009 6:51 pm

Nicola at work had never previously encountered polyhedra. I doodled a line drawing of the small stellated dodecahedron and she was fascinated,...

7 Replies

51366 Views

Last post by Peter Kane
Tue Mar 29, 2011 6:56 am
Isohedra with non-convex faces

Last post by marcelteun « Mon Jul 19, 2010 8:18 pm
Replies: 19
by oxenholme » Wed Sep 23, 2009 7:16 am
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2
My mathematics are sadly lacking. Has anybody here got the necessary mathematical ability to translate the equations and values in the paper...
19 Replies

102558 Views

Last post by marcelteun
Mon Jul 19, 2010 8:18 pm
Tintin-R

Last post by guy « Sat Feb 06, 2010 10:21 pm
Replies: 1
by marcelteun » Sat Feb 06, 2010 11:37 am

Hi,

My 4 year old son asked me to create a rocket polyhedron. I though I would share it with you.

:wink:

1 Replies

27965 Views

Last post by guy
Sat Feb 06, 2010 10:21 pm
Octahedron plus Dodecahedron

Last post by Nordehylop « Mon Dec 28, 2009 4:21 am
Replies: 1
by oxenholme » Sat Dec 26, 2009 6:41 pm

I spotted this among the compounds in Stella and had to make it. I tried using a multicolour octahedron and a plain grey dodecahedron. It looks super...

1 Replies

28860 Views

Last post by Nordehylop
Mon Dec 28, 2009 4:21 am
Polyhedral dog toy

Last post by jbuddenh « Sat Jan 24, 2009 2:31 pm
Replies: 3
by robertw » Sun Nov 23, 2008 11:28 am

Hi,

I just picked up a rubber first stellation of the rhombic dodecahedron at the supermarket, being marketed as a dog toy! :D Might be Australian...

3 Replies

39559 Views

Last post by jbuddenh
Sat Jan 24, 2009 2:31 pm
What was your introduction to polyhedra?

Last post by robertw « Sun Apr 13, 2008 5:12 pm
Replies: 21
by oxenholme » Sat Jan 19, 2008 6:58 am
1

2
Around 1961 form master Bert Robinson at Bradford Grammar School had some beautifully constructed polyhedra on display in the classroom - the four I...
21 Replies

121817 Views

Last post by robertw
Sun Apr 13, 2008 5:12 pm
Polyhedral puzzles

Last post by Jabe « Sun Mar 16, 2008 10:59 pm
Replies: 1
by robertw » Sun Mar 16, 2008 9:50 am

Hi folks,

I just put some new polyhedral puzzles up on my site:

See what you think, and feel free to discuss here :)

Rob.

1 Replies

28398 Views

Last post by Jabe
Sun Mar 16, 2008 10:59 pm
A Duality-related Question

Last post by polymorphic « Sun Mar 16, 2008 2:05 pm
Replies: 4
by Nordehylop » Thu Feb 28, 2008 9:15 pm

Can you take the faces of a polyhedron, along with the faces of its dual, and rearrange them into a new polyhedron? I noticed that you can with the...

4 Replies

40817 Views

Last post by polymorphic
Sun Mar 16, 2008 2:05 pm

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