Search found 87 matches
- Sun Aug 25, 2024 4:24 pm
- Forum: Polyhedra
- Topic: Edge-Transitive Polyhedra
- Replies: 10
- Views: 35287
Re: Edge-Transitive Polyhedra
These are fascinating to read about, and to examine the one thumbnail image which has been posted. They sound beautiful. But there is no polyhedron software which installs cleanly on my system and can view .off files equally cleanly. And Ulrich's image server is either broken or hates my system. The...
- Mon May 09, 2022 12:39 pm
- Forum: Stella Feature Requests
- Topic: Better rendering of infinite duals
- Replies: 9
- Views: 30515
Re: Better rendering of infinite duals
Looks good. Sorry to have fed you a red herring.
- Mon May 02, 2022 11:53 am
- Forum: Polyhedra
- Topic: How hard would it be to compute true filling?
- Replies: 8
- Views: 31266
Re: How hard would it be to compute true filling?
metachirality asked about regions suddenly flipping to a different density. I was trying to explain that using the conventional definition of a dense interior region, this cannot happen; as the polyhedron morphs, one region progressively gives way to another one of different density. A sudden flip ...
- Mon May 02, 2022 11:44 am
- Forum: Stella Feature Requests
- Topic: Better rendering of infinite duals
- Replies: 9
- Views: 30515
Re: Better rendering of infinite duals
I think there's only an issue when the centre of reciprocation lies in a facial plane (ie hemi faces). You'd get this issue even with convex polyhedra if you decide to put the centre of reciprocation on one of the faces. Nonconvex polyhedra work fine as long as they don't have hemi-faces. Isn't you...
- Mon May 02, 2022 11:35 am
- Forum: Stella Forum
- Topic: Facetings of a polyhedron
- Replies: 2
- Views: 16884
Re: Facetings of a polyhedron
Thank you. There seems to be a more or less "unlimited" option in there, excellent. Now I just need to get to grips with WINE. Yes, "tidy" is a term I introduced, but the whole point of it is that it has no rigorous definition - it is a rag-bag of intuitive notions, which sometimes lead to paradoxes...
- Sun May 01, 2022 5:37 pm
- Forum: Stella Feature Requests
- Topic: Better rendering of infinite duals
- Replies: 9
- Views: 30515
Re: Better rendering of infinite duals
I recall discussing this many years ago. The fundamental issue is that the "interior" of an infinite face is not defined. Polyhedral reciprocation is only equivalent to projective reciprocity for convex solids. Non-convexity introduces anomalies as to the filled-in bits of the face plane, and the so...
- Sun May 01, 2022 5:24 pm
- Forum: Polyhedra
- Topic: How hard would it be to compute true filling?
- Replies: 8
- Views: 31266
Re: How hard would it be to compute true filling?
https://i.postimg.cc/9FMSRjrM/image.png The issue here is, how do you define a "region"? When you pull apart the vertical and horizontal ends of the 4, are you pulling the horizontal away from the vertical, or are you pulling the vertical away from the horizontal? In each case, where does the regio...
- Sun May 01, 2022 4:40 pm
- Forum: Polyhedra
- Topic: Possible Wenninger Erratum
- Replies: 3
- Views: 18993
Re: Possible Wenninger Erratum
I have the 1989 reprint. It is definitely a mistake.
And it's not on my list at https://www.steelpillow.com//polyhedra/ ... inger.html
I'd better do a quick update.
Thank you for posting it here.
And it's not on my list at https://www.steelpillow.com//polyhedra/ ... inger.html
I'd better do a quick update.
Thank you for posting it here.
- Sun May 01, 2022 4:24 pm
- Forum: Stella Forum
- Topic: Facetings of a polyhedron
- Replies: 2
- Views: 16884
Facetings of a polyhedron
Hi Rob, Long time no see. Off and on I have been working on the underlying theory of polytopes, with a view to applying it to stellations and facetings. Now that I have at last got there, I am interested in enumerating the facetings of the regular dodecahedon in particular. (I published its faceting...
- Fri Nov 02, 2018 3:27 pm
- Forum: Stella Forum
- Topic: Announcing MoStella! Mobile app full of polyhedra.
- Replies: 3
- Views: 39196
Re: Announcing MoStella! Mobile app full of polyhedra.
Thanks for the heads-up, Rob.
- Sun Oct 07, 2018 11:24 am
- Forum: Stella Forum
- Topic: What is this particular model
- Replies: 2
- Views: 12184
Re: What is this particular model
It is basically a non-uniform morph of the rhombicosahedron. One way of making it would be to create a compound of the regular icosahedron and the rhombic triacontahedron, as a new compound polyhedron (I assume Great Stella can do that), and then explore its stellations.
- Sun Oct 07, 2018 10:50 am
- Forum: Stella Forum
- Topic: Announcing MoStella! Mobile app full of polyhedra.
- Replies: 3
- Views: 39196
Re: Announcing MoStella! Mobile app full of polyhedra.
Hi Rob, Just been playing with MoStella Free, so I thought I'd drop you a line. First time in many years that I have had a box to run one of your apps on natively, this time a Planet Gemini PDA running Android. Thoughts follow in random order: In faces+wireframe view, the frame tends to disappear al...
- Sat Sep 24, 2016 9:03 am
- Forum: Polyhedra
- Topic: Coloring of Snub Dodecahedron
- Replies: 3
- Views: 36070
Map colouring is a complex and difficult topic. The four-colour theorem, that to always avoid even edges meeting you need four colours, was first proved by a computer exhausting all the possibilities and, I think, more recently proved analytically. The problem you pose is way more complex. I think y...
- Wed Aug 10, 2016 8:49 am
- Forum: Polyhedron Models
- Topic: Quasicrystals
- Replies: 11
- Views: 59435
Very nice, congratulations and thank you for sharing. How about removing a few building blocks so that a central cavity connects to the outside? Besides looking cool, such "holey" crystals have found various applications as catalysts, molecular or atomic filters, etc. but I have never seen a quasicr...
- Tue Aug 09, 2016 9:01 am
- Forum: Polyhedron Models
- Topic: Quasicrystals
- Replies: 11
- Views: 59435
I understand what you were talking about, but for whatever reason the numbers were still not right. By the way, the solid in the middle between the two pyramids would be a triangular antiprism instead of square antiprism :) Would the length of the space diagonal always be equally divided by the 3 s...