Talk:Octahemioctahedron

Which image is to be preferred?[edit]

So does the octahemioctahedron have tetrahedral or octahedral symmetry? Professor M. Fiendish, Esq. 05:57, 30 August 2009 (UTC)[reply]

That's a good question! The Wythoff symbol GIVEN is tetrahedral symmetry. You can see the Wythoff_symbol#Summary_table for a b | c forms, (no right angles), has 3 face colors.

It might be possible (or likely?!) that a second Wythoff symbol exists with octahedral symmetry, BUT I've never seen such a list. Tom Ruen (talk) 21:33, 30 August 2009 (UTC)[reply]

Richard Klitzing page shows tetrahedral one, [1], with two sets of 4 triangles, AND an isotoxal (edge-transitive) table which groups all 8 triangles together, but I don't know what that means, whether there's a mirror construction for it!? Tom Ruen (talk) 21:35, 30 August 2009 (UTC)[reply]

3/2 3 | 3? That has tetrahedral symmetry, you're right. But since the octahemioctahedron is a facetting of the cuboctahedron, which has octahedral symmetry...I don't know. I'll try asking at the reference desk. Professor M. Fiendish, Esq. 12:53, 31 August 2009 (UTC)[reply]

I confirmed by email from Richard Klitzing that there is no octahedral symmetry construction for this polyhedron. Tom Ruen (talk) 21:23, 6 September 2009 (UTC)[reply]

Second Wythoff?[edit]

What's thh wythoff symbol for the octahedral construction? SockPuppetForTomruen (talk) 00:59, 21 August 2011 (UTC)[reply]

Tetrahedral: ³/₂ 3 | 3

Oho is a blend of co and cho. The p q (r s) | Wythoff symbols are blends, but are restricted to the polyhedra with vertex configurations p.q.-p.-q. I think another hack Wythoff symbol could work for an octahedral construction. Double sharp (talk) 03:58, 22 April 2012 (UTC)[reply]

...Looks like another hack has to be made, as there are no pairs of Wythoffian polyhedra of the form "oho+n{p/2q}" that are necessary if you want to be able to use a p q ^r
_s |-style Wythoff symbol. Double sharp (talk) 08:09, 23 March 2014 (UTC)[reply]

Symmetry Group[edit]

I think it needs to be made clear that this polyhedron has octahedral symmetry. It can only have tetrahedral symmetry if you allow oriented faces. Orientation of faces is a useful concept when considering Wythoff construction, or when studying the topology of a polyhedron, but it's an additional concept. Polyhedron faces, by definition, do not have orientations. Auximines (talk) 12:46, 15 January 2014 (UTC)[reply]

The stat table lists both. Its Wythoff construction is only tetrahedral symmetry. I added both symmetry images side-by-side to help. Feel free to describe more as you like. Tom Ruen (talk) 02:34, 16 January 2014 (UTC)[reply]

The cubohemioctahedron can also have tetrahedral symmetry. Why don't we show that too? Is it because oho's tetrahedral symmetry is its only possible Wythoff construction? To me that doesn't mean we should treat the Wythoff construction as primary: to me it means that the Wythoff construction is inadequate for a full description of this polyhedron. I tried to make the article treat oho's octahedral symmetry as primary. Better? Double sharp (talk) 07:41, 30 March 2014 (UTC)[reply]