Search found 148 matches

by Ulrich
Wed Dec 02, 2020 3:40 pm
Forum: Polyhedra
Topic: Two new noble polyhedra - a new source of convex hulls to search from?
Replies: 27
Views: 7731

Re: Two new noble polyhedra - a new source of convex hulls to search from?

Oh, sorry, you're right, it's the same. I didn't look carefully.
by Ulrich
Wed Dec 02, 2020 11:56 am
Forum: Polyhedra
Topic: Two new noble polyhedra - a new source of convex hulls to search from?
Replies: 27
Views: 7731

Re: Two new noble polyhedra - a new source of convex hulls to search from?

In the meantime I found one more pair. It is derived from an augmented dodecahedron:

Image

Image
by Ulrich
Wed Dec 02, 2020 8:16 am
Forum: Polyhedra
Topic: Two new noble polyhedra - a new source of convex hulls to search from?
Replies: 27
Views: 7731

Re: Two new noble polyhedra - a new source of convex hulls to search from?

I struggled with the cubic ones some time ago. Trying to reproduce Bückners 24,3 I faceted a rhombic cuboctahedron in a way Branko Grünbaum described years ago. In the preview window everything looks allright but if I hit shift ctrl F the face is splitted to coplanar triangles and I get 12 disphenoi...
by Ulrich
Mon Nov 30, 2020 7:34 am
Forum: Polyhedra
Topic: Two new noble polyhedra - a new source of convex hulls to search from?
Replies: 27
Views: 7731

Re: Two new noble polyhedra - a new source of convex hulls to search from?

Great!

I tried starting from geodesic spheres and many different bodies created with the morphing tools. Thus we get trillions of isogonal polyhedra but all isohedral facetings from these were crowns and disphenoids. All this is poking in the fog.

Ulrich
by Ulrich
Mon Nov 23, 2020 8:59 am
Forum: Polyhedra
Topic: Two new noble polyhedra - a new source of convex hulls to search from?
Replies: 27
Views: 7731

Re: Two new noble polyhedra - a new source of convex hulls to search from?

senkoquartz, your latest discoveries brought me to the following: I augmented the icosahedron with pyramids, faceted it isohedral and faceted the duals of the convex hulls of the results again. Thus I found four more noble polyhedra: https://i.postimg.cc/sBRmDPYB/Faceted-Stellated-Dual-of-Augmented-...
by Ulrich
Sat Nov 21, 2020 8:50 am
Forum: Polyhedra
Topic: Two new noble polyhedra - a new source of convex hulls to search from?
Replies: 27
Views: 7731

Re: Two new noble polyhedra - a new source of convex hulls to search from?

Ah, thanks, I got it now. The first one is really great with its pentagonal faces and I'm eager to build it in paper.

Ulrich
by Ulrich
Wed Nov 18, 2020 1:58 pm
Forum: Polyhedra
Topic: Two new noble polyhedra - a new source of convex hulls to search from?
Replies: 27
Views: 7731

Re: Two new noble polyhedra - a new source of convex hulls to search from?

I was not able to reproduce this with my equipment because stella always crashes when I try to create an isohedral faceting of the small retrosnub icosicosidodecahedron's dual or its convex hull. Could you describe how you managed to do so?

Thanks
Ulrich
by Ulrich
Sun Sep 27, 2020 7:27 am
Forum: Polyhedra
Topic: What are your favorite polyhedra?
Replies: 5
Views: 3144

Re: What are your favorite polyhedra?

These are beautiful models and very pretty polyhedra/polytopes! To me it is difficult to say which one is my favorite polyhedron. It changes all day and every model I finished is my favorite one for some time. In principle, I love all uniform ones. And one of my favorite is the rhombic triacontahedr...
by Ulrich
Fri Sep 18, 2020 8:37 am
Forum: Polyhedra
Topic: A list of every* isohedral triacontahedron, plus every* rigidly isohedral polyhedron, and a list of nobles
Replies: 7
Views: 3733

Re: A list of every* isohedral triacontahedron, plus every* rigidly isohedral polyhedron, and a list of nobles

Great work! Thanks for sharing.
I can hardly stop myself from building a paper model of 198 42 Rb immediately.
Others like 309 93 L or 301 85 L would be a challenge.

Ulrich
by Ulrich
Sat Aug 22, 2020 11:27 am
Forum: Polyhedron Models
Topic: What's the most complex model you've ever made?
Replies: 32
Views: 120166

Re: What's the most complex model you've ever made?

Very nice model, cool and elegant colouring.
Is it so that in the polyhedron always one edge must be
counted twice because two edges of one heptagon meet
there?
by Ulrich
Thu Jul 02, 2020 6:58 am
Forum: Polyhedra
Topic: Noble polyhedra. Where can I find them?
Replies: 17
Views: 10196

Re: Noble polyhedra. Where can I find them?

My paper about exploring noble polyhedra with Stella4D is now online at the Bridges Website:

http://archive.bridgesmathart.org/2020/ ... 20-257.pdf

Ulrich
by Ulrich
Sun Jun 07, 2020 7:51 am
Forum: Polyhedra
Topic: Noble polyhedra. Where can I find them?
Replies: 17
Views: 10196

Re: Noble polyhedra. Where can I find them?

It is that truncated icosidodecahedron problem that I mentioned above. Stella can‘t handle it because there are too many data. Some of the Brückner polyhedra with 120 vertices from the library can be used as source for new noble ones and stella doesn‘t crash. But all of them have only 60 vertices an...
by Ulrich
Sat Jun 06, 2020 6:24 am
Forum: Polyhedra
Topic: Noble polyhedra. Where can I find them?
Replies: 17
Views: 10196

Re: Noble polyhedra. Where can I find them?

Very nice! I could construct them from W115_01_d resp. W110_01_d.
The faces of your third one are very similar to those of W96_01_sd, but
the stellation diagram is different.

Ulrich
by Ulrich
Thu Jun 04, 2020 8:46 am
Forum: Polyhedron Models
Topic: A few pics
Replies: 28
Views: 21195

Re: A few pics

The second compound is really cool.
You had to cut and glue some very small facelets.

Ulrich
by Ulrich
Tue Jun 02, 2020 8:43 am
Forum: Polyhedra
Topic: Noble polyhedra. Where can I find them?
Replies: 17
Views: 10196

Re: Noble polyhedra. Where can I find them?

I was able to reproduce this, it‘s really nice. Unfortunately it is only isohedral.

I sent you a table with my noble findings the other day in a private message, so that you can compare your list with mine.

Ulrich