Pseudoicosahedron
Four views of the pseudoicosahedron, with eight equilateral triangles (red and yellow), and 12 blue isosceles triangles.
Faces	20 (8 equilateral triangles + 12 isosceles triangles)
Edges	30 (6 + 24)
Vertices	12
Symmetry group	Th, [4,3+], (3*2) (2 face colors) Td, [3,3]+, (332) (3 face colors)
Dual polyhedron	Pyritohedron
Properties	convex

A pseudoicosahedron is a twelve-sided polyhedron that can be regarded as a particular form of distorted regular icosahedron containing tetrahedral symmetry.

Cartesian coordinates

The coordinates of the 20 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).

This compares with the equivalent coordinates of a regular icosahedron, which can be generated by the same operations carried out starting with the vector (φ, 1, 0), where φ is the golden ratio.^[1]

Crystal pyrite

Iron pyrites have been observed to have formed crystals in the form of pseudoicosahedra.^[2]