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.

Read more about Triangular Orthobicupola:  Formulae