Parabidiminished rhombicosidodecahedron

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Parabidiminished rhombicosidodecahedron
Parabidiminished rhombicosidodecahedron.png
Type Johnson
J79 - J80 - J81
Faces 10 triangles
2×10 squares
10 pentagons
2 decagons
Edges 90
Vertices 50
Vertex configuration 20(4.5.10)
10+20(3.4.5.4)
Symmetry group D5d
Dual polyhedron -
Properties convex
Net
Johnson solid 80 net.png

In geometry, the parabidiminished rhombicosidodecahedron is one of the Johnson solids (J80).

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]

It can be constructed as a rhombicosidodecahedron with two opposing pentagonal cupolae removed. Related Johnson solids are the diminished rhombicosidodecahedron (J76) where one cupola is removed, the metabidiminished rhombicosidodecahedron (J81) where two non-opposing cupolae are removed and the tridiminished rhombicosidodecahedron (J83) where three cupolae are removed.

Example[edit]

Parabidiminished rhombicosidodecahedron
(Institute of Mathematics and Statistics, University of São Paulo)

External links[edit]

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