Talk:Hosohedron

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

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)

etymology

The prefix “hoso-” was invented by H.S.M. Coxeter, and possibly derives from the English “hose”.

Any reason not to presume it's Greek ὅσο– 'as much'? —Tamfang (talk) 03:46, 27 July 2009 (UTC)

No knowledge from me! Tom Ruen (talk) 04:33, 27 July 2009 (UTC)

Relation to Special Cases?

The redirection to here from the trihedron page seems to need some clarification, since this page (for hosohedron) does not include the term trihedron or a definition of the term trihedron. There is some information on MathWorld about the notion of a trihedron, but it is minimal. I hope that someone who knows about trihedra will add a page for them (or a section here...), because I wanted to know more about their groups of symmetries, which apparently are called "trihedral groups". Matt Insall 18:01, 8 July 2017 (UTC) — Preceding unsigned comment added by Espresso-hound (talk • contribs)

Coxeter?

In the section Etymology it says "The term 'hosohedron' was coined by H.S.M. Coxeter...". But according to Coxeter's Regular Complex Polytopes (1974, ISBN:052120125X) p. 20: "The hosohedron {2,p} (in a slightly distorted form) was named by Vito Caravelli (1724-1800), and the dihedron {p,2} by Felix Klein (1849-1925)." Episcophagus (talk) 09:16, 10 August 2019 (UTC)

See Vito Caravelli, Archimedis theoremata (1751) p. 152: "Liber tertius: De Hosoedris." -Episcophagus (talk) 09:37, 10 August 2019 (UTC)

Quite right AFAICT, @Episcophagus: the Schwartzman lemma referenced for the etymology doesn’t even mention HSMC (although I guess he may have ‘popularized’ the term). Any reason we shouldn’t cite Coxeter as above to credit Caravelli? Otherwise, although it would be WP:OR to say his was the first usage, I think per WP:PRIMARY & WP:BLUE we could say merely that it appears in his 1751 work.—Odysseus1479 01:45, 14 June 2021 (UTC)

@Odysseus1479:. Of course it is Caravelli who should be credited for introducing the term 'hosohedron' - and even HSM Coxeter agrees on this. Episcophagus (talk) 16:07, 14 June 2021 (UTC)

@Episcophagus:  Done.—Odysseus1479 23:08, 3 July 2021 (UTC)