Pentagonal orthobirotunda

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Pentagonal orthobirotunda
Pentagonal orthobirotunda.png
Type Johnson
J33 - J34 - J35
Faces 2.10 triangles
2+10 pentagons
Edges 60
Vertices 30
Vertex configuration 10(32.52)
2.10(3.5.3.5)
Symmetry group D5h
Dual polyhedron Trapezo-rhombic triacontahedron
Properties convex
Net
Johnson solid 34 net.png

In geometry, the pentagonal orthobirotunda is one of the Johnson solids (J34). It can be constructed by joining two pentagonal rotundae (J6) along their decagonal faces, matching like faces.

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]

Related polyhedra[edit]

The pentagonal orthobirotunda is also related to a Archimedean solid, the icosidodecahedron, which can also be called a pentagonal gyrobirotunda, similarly created by two pentagonal rotunda but with a 36-degree rotation.

Dissected icosidodecahedron.png
(Dissection)
Icosidodecahedron.png
Icosidodecahedron
(pentagonal gyrobirotunda)
Pentagonal orthobirotunda solid.png
Pentagonal orthobirotunda
Pentagonal rotunda.png
Pentagonal rotunda

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 .