Triangular Orthobicupola

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.

The triangular orthobicupola is the first in an infinite set of orthobicupolae.

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 elongated triangular orthobicupola (J₃₅), which is constructed by elongating this solid, has a (different) special relationship with the rhombicuboctahedron.

The 92 Johnson solids were named and described by Norman Johnson in 1966.

The dual of the triangular orthobicupola is called a trapezoid-rhombic dodecahedron. It has 6 rhombic and 6 trapezoidal faces. It is similar to the rhombic dodecahedron and both of them are space-filling polyhedra.