Talk:Convex regular 4-polytope

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I'm not sure why we have discussion of infinite regular tessellations and semiregular polytopes made from Platonic solids on this page. These topics don't really fall under the heading of convex regular 4-polytope. This content should probably be moved elsewhere, although I am not sure where. Any suggestions? -- Fropuff 01:24, 18 September 2005 (UTC)

• Agreed. I expected the new content to be split into a new article. Polytopes don't have as much agreed upon terminology as polyhedrons - where there's a whole slew of geometric categorical articles: Semiregular polyhedra Platonic solid Kepler-Poinsot solid Archimedean solid Prism (geometry) Antiprism Bipyramid Tilings of regular polygons
• I could make a new article called Semiregular 4-polytopes which would include the 6 regular polytopes as a subset. However I don't have an ennumeration of all the semiregular polytopes. I only have the subset made from regular polyhedral cells. The larger set includes semiregular polyhedral cells.
• My priority now is to add pictures for all of these shapes, but I'm still working on getting some nice symmetric projective views.
• Okay, I suppose there's no harm in a new article Semiregular 4-polytopes that includes the regular and finite tessellations as well. I'll do it.
• Tom Ruen 18:44, 18 September 2005 (UTC)

You know, I got to thinking a couple of days ago, if you truncated a pentachoron wouldn't it result in a regular 10 celled polychoron? You should also get a regular shape from truncating a 24-cell.

Hmmm... Thinking in 4D by extrapolating 2-3D is mentally taxing!

• 2D: A truncated triangle can be a hexagon (if edges cut in thirds). (3->6 sides)
• 3D: A truncation of a tetrahedron can be an octahedron (if edges fully cut). (4->8 faces)
• 4D: Perhaps the semiregular polychoron Rectified 5-cell (Dispentachoron or rectified 5-cell) can be seen as a truncated pentachoron. It has 5 octahedra and 5 tetrahedral cells. I can't see it exactly, but seems sensible!
• Tom Ruen 19:11, 3 October 2005 (UTC)

Yeah I thought about that but that would really be more like the 4 dimensional equivelent of the truncated tetrahedron. Perhaps a better example is in order, say you intersected two 5-cells and then cut off all the points. Since the vertex figure of the 5-cell is a tetrehedron you'd end up with a polychoron with 10 tetrehedral cells. -RyanAH

[edit] Symmetry groups

I'm glad for improvements. Any references to new symmetry group names? Existing header link not very helpful. Tom Ruen 20:08, 19 May 2006 (UTC)

The names refer to the finite Coxeter groups (as explained in the paragraph before the table). -- Fropuff 22:34, 19 May 2006 (UTC)

Got it, I added symbols to tables in regular polychora articles as well, and some of the uniform polychora linked at Uniform_polychoron. Tom Ruen 23:07, 19 May 2006 (UTC)