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This page doesn't display properly under IE 6, the graphics box completely obscures the main text. —Preceding unsigned comment added by 208.68.244.251 ( talk) 23:53, 1 April 2008 (UTC)
I just removed this from the stellation and quasiregular categories.
Firstly, it is not a stellation of any convex core.
Then, yes it has regular faces of two types alternating around each vertex. But there are more subtle issues which mean that it is not usually regarded as quasiregular. For example its vertex figure is sometimes written as {3.4.3/2.4}. Personally I think it should be (for an even more subtle reason), but that is not what the rest of the world thinks.
steelpillow 15:05, 8 January 2007 (UTC)
Have a look at the "elco" entry at Klitzing's page for Grünbaum–Coxeter polytopes: [1]. Double sharp ( talk) 13:51, 29 May 2012 (UTC)
I don't see anything wrong with my edit. My open-link edits like this were done over about 30 articles, getting started linking some common terminology, still useful even without linked-article yet. I purposely removed the vertex/edge counts since it includes ALL of them, left the face info since only half of triangle are shared. Tom Ruen 21:07, 11 May 2007 (UTC) See: Special:Whatlinkshere/Edge_arrangement and Special:Whatlinkshere/Vertex_arrangement.
It looks nice, but I don't quite see where the square faces are. -- Johanneskepler ( talk) 03:00, 10 August 2009 (UTC)
This article claimed that the tetrahemihexahedron was the three-dimensional “demicross” polytope. I’ve commented out that claim, since I can’t find any other source replicating it, which violates WP:OR. However, it’s interesting to try to interpret that claim. Here’s my guess, which will hopefully inspire someone else to look into the matter further (and possibly even create a citation for that claim?)
By the same reason an n- hypercube’s vertices can be 2-colored, any n- hyperoctahedron’s facets can too. Furthermore, if we remove any two opposite vertices from an n-hyperoctahedron, we get an (n − 1)-hyperoctahedron’s vertices. We can then create an n-polytope with these two sets of (n − 1)-polytopes. I believe that this is what a demicross polytope is supposed to be.
Under this assumption, the demicross 2-polytope would be a crossed quadrilateral with the vertices of a square, and the demicross 3-polytope would effectively be the tetrahemihexahedron. The demicross 4-polytope would consist of 8 tetrahedra and 4 octahedra (and would in fact correspond to what Bowers has dubbed the tesseracthemioctachoron. The demicross 5-polytope would consist of 16 5-cells and 5 16-cells (and correspond to Bowers’ hexadecahemidecateron. And so on.
Seems like an interesting family, it’s a shame that uniform polytopes are still such an obscure field of study. OfficialURL ( talk) 06:21, 30 March 2020 (UTC)
![]() | This article is rated Start-class on Wikipedia's
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This page doesn't display properly under IE 6, the graphics box completely obscures the main text. —Preceding unsigned comment added by 208.68.244.251 ( talk) 23:53, 1 April 2008 (UTC)
I just removed this from the stellation and quasiregular categories.
Firstly, it is not a stellation of any convex core.
Then, yes it has regular faces of two types alternating around each vertex. But there are more subtle issues which mean that it is not usually regarded as quasiregular. For example its vertex figure is sometimes written as {3.4.3/2.4}. Personally I think it should be (for an even more subtle reason), but that is not what the rest of the world thinks.
steelpillow 15:05, 8 January 2007 (UTC)
Have a look at the "elco" entry at Klitzing's page for Grünbaum–Coxeter polytopes: [1]. Double sharp ( talk) 13:51, 29 May 2012 (UTC)
I don't see anything wrong with my edit. My open-link edits like this were done over about 30 articles, getting started linking some common terminology, still useful even without linked-article yet. I purposely removed the vertex/edge counts since it includes ALL of them, left the face info since only half of triangle are shared. Tom Ruen 21:07, 11 May 2007 (UTC) See: Special:Whatlinkshere/Edge_arrangement and Special:Whatlinkshere/Vertex_arrangement.
It looks nice, but I don't quite see where the square faces are. -- Johanneskepler ( talk) 03:00, 10 August 2009 (UTC)
This article claimed that the tetrahemihexahedron was the three-dimensional “demicross” polytope. I’ve commented out that claim, since I can’t find any other source replicating it, which violates WP:OR. However, it’s interesting to try to interpret that claim. Here’s my guess, which will hopefully inspire someone else to look into the matter further (and possibly even create a citation for that claim?)
By the same reason an n- hypercube’s vertices can be 2-colored, any n- hyperoctahedron’s facets can too. Furthermore, if we remove any two opposite vertices from an n-hyperoctahedron, we get an (n − 1)-hyperoctahedron’s vertices. We can then create an n-polytope with these two sets of (n − 1)-polytopes. I believe that this is what a demicross polytope is supposed to be.
Under this assumption, the demicross 2-polytope would be a crossed quadrilateral with the vertices of a square, and the demicross 3-polytope would effectively be the tetrahemihexahedron. The demicross 4-polytope would consist of 8 tetrahedra and 4 octahedra (and would in fact correspond to what Bowers has dubbed the tesseracthemioctachoron. The demicross 5-polytope would consist of 16 5-cells and 5 16-cells (and correspond to Bowers’ hexadecahemidecateron. And so on.
Seems like an interesting family, it’s a shame that uniform polytopes are still such an obscure field of study. OfficialURL ( talk) 06:21, 30 March 2020 (UTC)