Triangular orthobicupola

Infobox Polyhedron


Polyhedron_Type=Johnson
"J"₂₆ - J₂₇ - J₂₈
Face_List=2+6 triangles
6 squares
Edge_Count=24
Vertex_Count=12
Symmetry_Group=D_3h
Vertex_List=6(3².4²)
6(3.4.3.4)
Dual=Trapezo-rhombic dodecahedron
Property_List=convex

In geometry, the triangular orthobicupola is one of the Johnson solids ("J"₂₇). As the name suggests, it can be constructed by attaching two triangular cupolas ("J"₃) along their bases. It has an equal number of squares and triangles at each vertex; however, it is not vertex-transitive.

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.

The elongated triangular orthobicupola ("J"₃₅), 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.

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