Pentagonal orthobirotunda

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Pentagonal orthobirotunda
Pentagonal orthobirotunda.png
TypeJohnson
J33 - J34 - J35
Faces2x10 triangles
2+10 pentagons
Edges60
Vertices30
Vertex configuration10(32.52)
2.10(3.5.3.5)
Symmetry groupD5h
Dual polyhedronTrapezo-rhombic triacontahedron
Propertiesconvex
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 is composed of regular polygon faces but are not uniform polyhedra (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 an 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.