Parabidiminished rhombicosidodecahedron

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Parabidiminished rhombicosidodecahedron
Parabidiminished rhombicosidodecahedron.png
TypeJohnson
J79 - J80 - J81
Faces10 triangles
2×10 squares
10 pentagons
2 decagons
Edges90
Vertices50
Vertex configuration20(4.5.10)
10+20(3.4.5.4)
Symmetry groupD5d
Dual polyhedron-
Propertiesconvex
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, doi:10.4153/cjm-1966-021-8, MR 0185507, Zbl 0132.14603.