Tridiminished icosahedron

From Wikipedia, the free encyclopedia
Jump to: navigation, search
Tridiminished icosahedron
Tridiminished icosahedron.png
Type Johnson
J62 - J63 - J64
Faces 2+3 triangles
3 pentagons
Edges 15
Vertices 9
Vertex configuration 2x3(3.52)
Symmetry group C3v
Dual polyhedron Dual of tridiminished icosahedron (unnamed enneahedron)
Properties convex
Johnson solid 63 net.png

In geometry, the tridiminished icosahedron is one of the Johnson solids (J63).

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 three pentagonal pyramids from a regular icosahedron, which replaces three sets of five triangular faces from the icosahedron with three mutually adjacent pentagonal faces.

Related polytopes[edit]

The tridiminished icosahedron is the vertex figure of the snub 24-cell, a uniform 4-polytope (4-dimensional polytope).

See also[edit]

External links[edit]

  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 .