Parabiaugmented dodecahedron

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Parabiaugmented dodecahedron
Parabiaugmented dodecahedron.png
Type Johnson
J58 - J59 - J60
Faces 10 triangles
10 pentagons
Edges 40
Vertices 22
Vertex configuration 10(53)
10(32.52)
2(35)
Symmetry group D5d
Dual polyhedron -
Properties convex
Net
Johnson solid 59 net.png

In geometry, the parabiaugmented dodecahedron is one of the Johnson solids (J59). It can be seen as a dodecahedron with two pentagonal pyramids (J2) attached to opposite faces. When pyramids are attached to a dodecahedron in other ways, they may result in an augmented dodecahedron, a metabiaugmented dodecahedron, a triaugmented dodecahedron, or even a pentakis dodecahedron if the faces are made to be irregular.

The dual of this solid is the Gyroelongated pentagonal bifrustum. 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 solid s, Archimedean solid s, prism s, or antiprism s). They were named by Norman Johnson , who first listed these polyhedra in 1966. [1]

  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 .

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