J26 - J27 - J28
|Dual polyhedron||Trapezo-rhombic dodecahedron|
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.
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.
The triangular orthobicupola is the first in an infinite set of orthobicupolae.
Relation to cuboctahedra
|Triangular orthobicupola||Triangular gyrobicupola|
|Both the triangular orthobicupola and the cuboctahedron (triangular gyrobicupola) contain a central regular hexagon. They can be dissected on this hexagon into pairs of triangular cupolae.|
The triangular orthobicupola has a superficial resemblance to the cuboctahedron, which would be known as the triangular gyrobicupola in the nomenclature of Johnson solids — the difference is that the two triangular cupolas which make up the triangular orthobicupola are joined so that pairs of matching sides abut (hence, "ortho"); the cuboctahedron is joined so that triangles abut squares and vice versa. Given a triangular orthobicupola, a 60-degree rotation of one cupola before the joining yields a cuboctahedron. Hence, another name for the triangular orthobicupola is the anticuboctahedron.
The circumradius of a triangular orthobicupola is the same as the edge length (C=a).
Related polyhedra and honeycombs
- 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.
- Stephen Wolfram, "Triangular orthobicupola" from Wolfram Alpha. Retrieved July 23, 2010.
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