Icosahedron
polyhedron with 20 faces
In geometry, an icosahedron ( or ) is a polyhedron with 20 faces. The name comes from Ancient Greek εἴκοσι (eíkosi) 'twenty' and ἕδρα (hédra) 'seat'. The plural can be either "icosahedra" () or "icosahedrons".
There are infinitely many non-similar shapes of icosahedra, some of them being more symmetrical than others. The best known is the (convex, non-stellated) regular icosahedron—one of the Platonic solids—whose faces are 20 equilateral triangles.
Regular icosahedra
There are two objects, one convex and one nonconvex, that can both be referred to as regular icosahedra, characterized by 30 edges and 20 triangular faces. The term "regular icosahedron" generally refers to a convex polyhedron, both a deltahedron and a Platonic solid; it is also called "icosahedron" for a plain term. A non-convex polyhedron version is the great icosahedron, a Kepler–Poinsot polyhedron. Both have icosahedral symmetry.
There are 59 stellations of a regular icosahedron (including the original icosahedron itself) according to Coxeter et al.
This brief starts where responsible research should: with the source description of “Icosahedron” as polyhedron with 20 faces. Everything that follows is an evidence route, not borrowed authority.
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Named sources, stable identifiers and responsible institutions provide the strongest route from overview to verifiable evidence. The source revision retrieved here is dated Jun 29, 2026. The linked authority identifier is Q188758. The Library of Congress control number is sh85064098. 1 of 1 selected statements include explicit references; 0 carry qualifiers and 0 use preferred rank.
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This entry incorporates text from “Icosahedron” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.