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.

They were named by Norman Johnson, who first listed these polyhedra in 1966.

Similar to the cuboctahedron, which would be known as the triangular gyrobicupola, the difference is that the two triangular cupolas that 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.

[3] Because the triangular orthobicupola has the property of convexity and its faces are regular polygons—eight equilateral triangles and six squares—it is categorized as a Johnson solid.

Its surface area can be obtained by summing all of its polygonal faces, and its volume is by slicing it off into two triangular cupolas and adding their volume.

The dual polyhedron of a triangular orthobicupola is the trapezo-rhombic dodecahedron.