Search found 13 matches

by senkoquartz
Thu Aug 06, 2020 9:58 am
Forum: Polyhedra
Topic: Polyhedral Chess Set
Replies: 5
Views: 18293

Re: Polyhedral Chess Set

Yeah, IMO, I think stella octangula would totally be the best choice for knight. A cuboctahedron clashes because all the others are regular. A stella octangula is regular, and also fits because pawns/tetrahedra are the smallest/simplest pieces, kings+queens/dodeca+icosa are the most important/comple...
by senkoquartz
Thu Aug 06, 2020 4:19 am
Forum: Polyhedra
Topic: Polyhedral Chess Set
Replies: 5
Views: 18293

Re: Polyhedral Chess Set

Knight could be a tetrahemihexahedron maybe? Or a stella octangula. As for king vs. queen and icosa vs. dodeca, a rook and cube are sort of more masculine than a bishop and octahedron, so that would carry over to rook->king and bishop->queen, and dodeca corresponds to cube while icosa goes with octa...
by senkoquartz
Wed Aug 05, 2020 2:00 pm
Forum: Polyhedra
Topic: Noble polyhedra. Where can I find them?
Replies: 16
Views: 2104

Re: Noble polyhedra. Where can I find them?

Also, regarding rigidly symmetrical polyhedra - There are only three shapes I know of that are both rigidly isogonal AND rigidly isohedral, and only one is a non-compound. The Bruckner catalogue's Stellated Icosahedron B is the non-compound. Because it's both a dodecahedron faceting and an icosahedr...
by senkoquartz
Wed Aug 05, 2020 1:29 pm
Forum: Polyhedra
Topic: Noble polyhedra. Where can I find them?
Replies: 16
Views: 2104

Re: Noble polyhedra. Where can I find them?

Returning to this topic, having to sift through Bruckner's catalogue to find non-compounds and non-repeats initially left we with a disinterest for noble compounds, but now I'm getting interested in them. I'm surprised to learn: disphenoids can be self-dual, self-dual disphenoids can form noble comp...
by senkoquartz
Thu Jun 25, 2020 7:03 pm
Forum: Stella Forum
Topic: Excluding facetings where the face's vertices lie on its edges?
Replies: 2
Views: 631

Re: Excluding facetings where the face's vertices lie on its edges?

but alas, the thread title should say "facetings where the DUAL'S face's vertices lie on its edges"
by senkoquartz
Thu Jun 25, 2020 6:01 pm
Forum: Stella Forum
Topic: Excluding facetings where the face's vertices lie on its edges?
Replies: 2
Views: 631

Excluding facetings where the face's vertices lie on its edges?

I was searching for isohedral triacontahedra by faceting the icosidodecahedron and checking its duals. But 95% of them end up having faces with verts lying on their own edges. Is there a way to skip over these?
by senkoquartz
Wed Jun 17, 2020 8:42 pm
Forum: Polyhedra
Topic: Noble polyhedra. Where can I find them?
Replies: 16
Views: 2104

Re: Noble polyhedra. Where can I find them?

*regarding that last question - i mean when I go through the 227 rhombic triacontahedron stellations for example, they outwardly look like isohedra but the faces are broken up
by senkoquartz
Wed Jun 17, 2020 8:34 pm
Forum: Polyhedra
Topic: Noble polyhedra. Where can I find them?
Replies: 16
Views: 2104

Re: Noble polyhedra. Where can I find them?

For the past day I've been interested in rigidly symmetrical polyhedra in general. (I'll be ignoring infinite dihedral families here.) There are countless types of isogonal polyhedra (and their isohedral duals), but the ones that are rigid and lose their transitivity when distorted seem more unique ...
by senkoquartz
Sat Jun 06, 2020 1:34 pm
Forum: Polyhedra
Topic: Noble polyhedra. Where can I find them?
Replies: 16
Views: 2104

Re: Noble polyhedra. Where can I find them?

@Ulrich Oh, I forgot - there was also this dodecahedron facet dual pair with degen vertices https://i.postimg.cc/c6sF9ppS/doe-facet.png I'm interested in finding nobles with 120 vertices. When I try to facet a polyhedron with 120 vertices, Stella puts up a heroic effort but crashes before finishing ...
by senkoquartz
Thu Jun 04, 2020 2:53 pm
Forum: Polyhedra
Topic: Noble polyhedra. Where can I find them?
Replies: 16
Views: 2104

Re: Noble polyhedra. Where can I find them?

@Ulrich When I said I found 46, I wasn't counting regular polyhedra and ones with degenerate faces - of which there are 17. So I actually have 3 new ones for you. The first two are a dual pair with hexagram faces - the first one has the same convex hull as your W115_01_d in the .pdf sent me, and the...
by senkoquartz
Sun May 31, 2020 11:47 pm
Forum: Polyhedra
Topic: Noble polyhedra. Where can I find them?
Replies: 16
Views: 2104

Re: Noble polyhedra. Where can I find them?

@Ulrich
I followed the above method - found 46 total.

There is a weird shape - not a noble - from faceting the 2 snub cubes compound. Face is a 7gon, with 2 types of vertices.
by senkoquartz
Sun May 24, 2020 1:36 am
Forum: Polyhedra
Topic: Noble polyhedra. Where can I find them?
Replies: 16
Views: 2104

Re: Noble polyhedra. Where can I find them?

@robertw I bought it, and I'm enjoying it a lot. In the Bruckner catalogue, after sifting through compounds and dual entries, I count 27 distinct nobles with octahedral or icosahedral symmetry, not including another 8 with degenerate hexagonal faces. In another thread you mentioned that you found a ...
by senkoquartz
Wed May 20, 2020 2:01 pm
Forum: Polyhedra
Topic: Noble polyhedra. Where can I find them?
Replies: 16
Views: 2104

Noble polyhedra. Where can I find them?

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 made out of ENNEAGRAMS. THAT'S INSANE. Now my mission in life is to learn about all the noble polyhedra I can. What I'm interested in are the "miscellane...