Talk:Hosohedron

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[edit] Only defined when digons are spherical lunes?

According to the MathWorld article, hosohedra are constructed of spherical lunes and have only two vertices. The Wikipedia article omits this information in the introductory paragraph, relegating it to a later paragraph describing the instance of a hosohedron as a spherical tesselation. Are there other possiblities? If not, I suggest incorporating that information into the introduction to improve clarity. andersonpd 19:38, 3 August 2006 (UTC)

The Coxeter reference also only mentions hosohedrons only in the context of spherical and "unbounded nonorientable" surfaces (pp 12, 68). Apparently, this is the definition, and I can't find any citations of the "degenerate polyhedron" meaning. Page edited to reflect this. Thanks for the petulancy; it's always appreciated. Phildonnia

[edit] Multidimensional analogues?

This text is given:

The 4-dimensional analogue is called a hosochoron (plural: hosochora). For example, {3,3,2} is a tetrahedral hosochoron.

Any references for this?! ALSO, I'd expect {3,3,2} would be a tetrahedral dichoron, parallel to a {3,2} triangular dihedron. Tom Ruen 21:01, 5 October 2006 (UTC)

Only reference I can find is:

• [1] - H.S.M. Coxeter's term for a polytope with two vertices. Such are the duals to ditopes.
• [2] A polytope with two [facets], the dual of a hosotope. (I substituted facet for face in reference)

So I think {p,q,...,2} is a regular ditope (2 {p,q,...} facets), and {2,...,q,p}, the dual, is perhaps a regular hosohedron (2 vertices)?

Since no one else seems to be watching this page I 'corrected the hosotope section best I could, but I don't think the naming is clearly rational - {2,3,3} has a tetrahedral vertex figure at least. I didn't look back who added it - perhaps should just be removed. Tom Ruen 07:57, 29 November 2006 (UTC)