27th Johnson solid; 2 triangular cupolae joined base-to-base
Triangular orthobicupola
Type
Johnson J26 – J27 – J28
Faces
2+6 triangles 6 squares
Edges
24
Vertices
12
Vertex configuration
6(32.42) 6(3.4.3.4)
Symmetry group
D3h
Dual polyhedron
Trapezo-rhombic dodecahedron
Properties
convex
Net
In geometry, the triangular orthobicupola is one of the Johnson solids (J27). As the name suggests, it can be constructed by attaching two triangular cupolas (J3) along their bases. It has an equal number of squares and triangles at each vertex; however, it is not vertex-transitive. It is also called an anticuboctahedron, twisted cuboctahedron or disheptahedron. It is also a canonical polyhedron.
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]
The triangular orthobicupola is the first in an infinite set of orthobicupolae.
^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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