page_title: Icosahedron
section_title: Cartesian coordinates
hierarchical_section_title: Icosahedron / Pyritohedral symmetry / Cartesian coordinates
caption_attribution_description: en:Peudoicosahedron
context_page_description: In geometry, an icosahedron is a polyhedron with 20 faces. The name comes from Ancient Greek εἴκοσι, meaning 'twenty', and ἕδρα, meaning '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 regular icosahedron—one of the Platonic solids—whose faces are 20 equilateral triangles.
context_section_description: The coordinates of the 12 vertices can be defined by the vectors defined by all the possible cyclic permutations and sign-flips of coordinates of the form (2, 1, 0). These coordinates represent the truncated octahedron with alternated vertices deleted.
  This construction is called a snub tetrahedron in its regular icosahedron form, generated by the same operations carried out starting with the vector (ϕ, 1, 0), where ϕ is the golden ratio.
caption: Construction from the vertices of a truncated octahedron, showing internal rectangles.
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