Search found 86 matches

by guy
Mon May 09, 2022 12:39 pm
Forum: Stella Feature Requests
Topic: Better rendering of infinite duals
Replies: 9
Views: 25195

Re: Better rendering of infinite duals

Looks good. Sorry to have fed you a red herring.
by guy
Mon May 02, 2022 11:53 am
Forum: Polyhedra
Topic: How hard would it be to compute true filling?
Replies: 8
Views: 26972

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 ...
by guy
Mon May 02, 2022 11:44 am
Forum: Stella Feature Requests
Topic: Better rendering of infinite duals
Replies: 9
Views: 25195

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...
by guy
Mon May 02, 2022 11:35 am
Forum: Stella Forum
Topic: Facetings of a polyhedron
Replies: 2
Views: 14673

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...
by guy
Sun May 01, 2022 5:37 pm
Forum: Stella Feature Requests
Topic: Better rendering of infinite duals
Replies: 9
Views: 25195

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...
by guy
Sun May 01, 2022 5:24 pm
Forum: Polyhedra
Topic: How hard would it be to compute true filling?
Replies: 8
Views: 26972

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...
by guy
Sun May 01, 2022 4:40 pm
Forum: Polyhedra
Topic: Possible Wenninger Erratum
Replies: 3
Views: 16444

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.
by guy
Sun May 01, 2022 4:24 pm
Forum: Stella Forum
Topic: Facetings of a polyhedron
Replies: 2
Views: 14673

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...
by guy
Fri Nov 02, 2018 3:27 pm
Forum: Stella Forum
Topic: Announcing MoStella! Mobile app full of polyhedra.
Replies: 3
Views: 36271

Re: Announcing MoStella! Mobile app full of polyhedra.

Thanks for the heads-up, Rob.
by guy
Sun Oct 07, 2018 11:24 am
Forum: Stella Forum
Topic: What is this particular model
Replies: 2
Views: 10564

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.
by guy
Sun Oct 07, 2018 10:50 am
Forum: Stella Forum
Topic: Announcing MoStella! Mobile app full of polyhedra.
Replies: 3
Views: 36271

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...
by guy
Sat Sep 24, 2016 9:03 am
Forum: Polyhedra
Topic: Coloring of Snub Dodecahedron
Replies: 3
Views: 33118

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...
by guy
Wed Aug 10, 2016 8:49 am
Forum: Polyhedron Models
Topic: Quasicrystals
Replies: 11
Views: 54178

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...
by guy
Tue Aug 09, 2016 9:01 am
Forum: Polyhedron Models
Topic: Quasicrystals
Replies: 11
Views: 54178

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...
by guy
Mon Aug 08, 2016 9:04 am
Forum: Polyhedron Models
Topic: Quasicrystals
Replies: 11
Views: 54178

The trick is to choose the right slices through the 3D object. It is easiest to explain for the cube. Pick one vertex and identify the three adjacent ones. Cut round these three to remove a triangular pyramid. Do the same on the opposite side so you now have two pyramids and a square antiprism. Thes...