Talk:Icosahedron
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regular icosahedron
It says
- "The most symmetrical are the two kinds of regular icosahedron. Each has 20 equilateral triangle faces with five meeting at each of its twelve vertices."
This statement is mysterious, and unless I missed it regular icosahedron only mentions one kind. I guess the other one is some sort of non-convex imbedding, but that needs a description plus a citation for it being also called "regular icosahedron". McKay (talk) 05:00, 31 August 2015 (UTC)
- The two kinds are described and illustrated immediately following the sentence you quote. This is one of those logical hiccups with language that mathematicians are so blind to. By common custom the name "regular icosahedron" is applied to the convex "Platonic" variety. But technically the description "regular icosahedron" includes both forms. This is not helped by the fact that in more theoretical formulations both are the same combinatorial or abstract construct and are morphs of each other: topologically, there is only one regular icosahedron. It would naturally help if the mathematical community were to more rigorously name the convex variety accordingly, but they do not care to see a problem. Consequently, citable sources are sorely lacking. For the encyclopedist of course, the problem is to make clear whether each instance of the phrase "regular icosahedron" is being used as a name or a description. I have amended the text to help clarify it a little. — Cheers, Steelpillow (Talk) 08:36, 31 August 2015 (UTC)
- The other one is the great icosahedron, which indeed has the same abstract structure as the convex regular icosahedron. The problem is that the term "regular icosahedron" appears to have become a term of its own whose meaning is not strictly that which would result from modifying the noun "icosahedron" with the adjective "regular"; the same may be said of "regular dodecahedron" (since there are four regular dodecahedra, only one of which is convex). Double sharp (talk) 06:06, 16 January 2018 (UTC)
- The two kinds are described and illustrated immediately following the sentence you quote. This is one of those logical hiccups with language that mathematicians are so blind to. By common custom the name "regular icosahedron" is applied to the convex "Platonic" variety. But technically the description "regular icosahedron" includes both forms. This is not helped by the fact that in more theoretical formulations both are the same combinatorial or abstract construct and are morphs of each other: topologically, there is only one regular icosahedron. It would naturally help if the mathematical community were to more rigorously name the convex variety accordingly, but they do not care to see a problem. Consequently, citable sources are sorely lacking. For the encyclopedist of course, the problem is to make clear whether each instance of the phrase "regular icosahedron" is being used as a name or a description. I have amended the text to help clarify it a little. — Cheers, Steelpillow (Talk) 08:36, 31 August 2015 (UTC)
D20
Should we note somewhere that the Icosahedron is used as twenty sided dice, which is probably the second most well known dice? TheKing44 (talk) 05:46, 16 January 2018 (UTC)
- That's already mentioned on regular icosahedron. Double sharp (talk) 06:03, 16 January 2018 (UTC)
Coordinates from truncated octahedron
It is not clearly stated that "deleting alternated vertices of truncated octahedron" gives a regular icosahedron.
The golden ratio one is regular, though.
Simple Symbol (talk) 22:07, 7 October 2021 (UTC)