Talk:Near-miss Johnson solid

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[edit] possible vertices

I'm missing something somewhere. It's "obvious" that two regular triangles cannot form a vertex with a third polygon whose angle is 2π/3 or more; and yet the vertex figure \cos{\frac{\pi}{3}} : \cos{\frac{\pi}{3}} : \cos{\frac{\pi}{N}} obeys the triangle inequality for all N. Can you show me the vertex figures for 3.3.6, 3.3.7? —Tamfang 19:18, 2 April 2006 (UTC)

Sorry, I see I was wrong in listing existence merely by positive angle defects, but I missed requirement that internal angle of only face can't exceed sum of angles of the other two faces! No time now for me to check again now, so if you're happy with what you changed (that I reverted), I trust your corrections. Tom Ruen 02:19, 4 April 2006 (UTC)
Incidentally, a while ago I made a test article listing vertex figures used in the uniform and johnson solids. A better article would link them all to articles, but a bit of a pain to complete links to all the long formal names. User:Tomruen/Polyhedra_by_vertex_figures. Tom Ruen 02:29, 4 April 2006 (UTC)

[edit] vocabulary

I used the word compound for the eleven Js that contain a rotunda. Is there a better word? —Tamfang 20:39, 20 May 2006 (UTC)

Hmmmm... Looking at Johnson solid terminology, seems like augmented or augumentations may be the most general term. Tom Ruen 05:13, 21 May 2006 (UTC) ... WELL, looking again, Augmented means that a pyramid or cupola has been joined to a face of the solid in question. is limited, but seems as good as anything. Tom Ruen 05:18, 21 May 2006 (UTC)
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