Talk:Deltahedron

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Polyhedra

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Image?

If somebody could find/generate an image with all of the deltahedrons displayed, that would make this page far more useful and comprehensible.Matt gies 23:46, 28 Feb 2004 (UTC)

18-faced deltahedron

Any proof that we can't have an 18-face deltahedron where some vertexes have 5 and some have 4?? Georgia guy (talk) 21:59, 1 May 2014 (UTC)[reply]

It's easy to list all the topologies with valences <6; none of them have 11 vertices. —Tamfang (talk) 05:46, 4 May 2014 (UTC)[reply]

I wonder where I buried that list! —Tamfang (talk) 07:57, 9 October 2024 (UTC)[reply]

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circumspheres

I am uneasy about saying the deltahedra appear in solutions of the Thomson problem and Tammes problem. Only the three regulars have vertices all lying on a sphere! Some other solutions have convex hulls topologically equivalent to the convex deltahedra, but these are not deltahedra. —Tamfang (talk) 22:45, 4 September 2024 (UTC)[reply]

Okay. I will remove it. Dedhert.Jr (talk) 01:48, 5 September 2024 (UTC)[reply]

convexity

A non-convex deltahedron is a deltahedron that does not possess convexity, meaning it has coplanar faces or collinear edges.

Consider an octahedron and an icosahedron sharing a face. Are they not a non-convex deltahedron? Do they have coplanar faces or collinear edges?

A figure with coplanar faces may still be convex, but not strictly convex like the eight. —Tamfang (talk) 19:19, 14 September 2024 (UTC)[reply]

Hmm! Some sources use "strictly convex", whereas Cundy and Litchenberg sources use "convex" instead to classify those eights. Google Scholars shows the "strictly convex deltahedron" but they do not explain what are those specifically, and the worst part is, Google Books does not shows anything about "strictly convex", [1] but "convex" instead [2]. Dedhert.Jr (talk) 00:45, 15 September 2024 (UTC)[reply]