# Metabidiminished icosahedron

Metabidiminished icosahedron
Type Johnson
J61 - J62 - J63
Faces 3x2+4 triangles
2 pentagons
Edges 20
Vertices 10
Vertex configuration 2(3.52)
2+4(33.5)
2(35)
Symmetry group C2v
Dual polyhedron -
Properties convex
Net

In geometry, the metabidiminished icosahedron is one of the Johnson solids (J62).

A Johnson solid is one of 92 strictly convex polyhedra that have regular faces but are not uniform (that is, they are not Platonic solids, Archimedean solids, prisms or antiprisms). They were named by Norman Johnson, who first listed these polyhedra in 1966.[1]

The name refers to one way of constructing it, by removing two pentagonal pyramids from a regular icosahedron, replacing two sets of five triangular faces of the icosahedron with two adjacent pentagonal faces. If two pentagonal pyramids are removed to form nonadjacent pentagonal faces, the result is instead the pentagonal antiprism.

1. Johnson, Norman W. (1966), "Convex polyhedra with regular faces", Canadian Journal of Mathematics, 18: 169–200, doi:10.4153/cjm-1966-021-8, MR 0185507, Zbl 0132.14603.