Parabiaugmented hexagonal prism

In geometry, the parabiaugmented hexagonal prism is one of the Johnson solids (J55). As the name suggests, it can be constructed by doubly augmenting a hexagonal prism by attaching square pyramids (J1) to two of its nonadjacent, parallel (opposite) equatorial faces. Attaching the pyramids to nonadjacent, nonparallel equatorial faces yields a metabiaugmented hexagonal prism (J56). (The solid obtained by attaching pyramids to adjacent equatorial faces is not convex, and thus not a Johnson solid.)

Parabiaugmented hexagonal prism
TypeJohnson
J54J55J56
Faces2x4 triangles
4 squares
2 hexagons
Edges26
Vertices14
Vertex configuration4(42.6)
2(34)
8(32.4.6)
Symmetry groupD2h
Dual polyhedronparabilaterotruncated hexagonal bipyramid
Propertiesconvex
Net

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]

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  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.