| Type: | Johnson |
| Faces: | 2+6 triangles 6 squares |
| Edges: | 24 |
| Vertices: | 12 |
| Dual: | Trapezo-rhombic dodecahedron |
| Properties: | convex |
| Net: | Johnson solid 27 net.png |
In geometry, the triangular orthobicupola is one of the Johnson solids . As the name suggests, it can be constructed by attaching two triangular cupolas 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. It is also a canonical polyhedron.
The triangular orthobicupola is the first in an infinite set of orthobicupolae.
The triangular orthobicupola can be constructed by attaching two triangular cupolas onto their bases. 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. Hence, another name for the triangular orthobicupola is the anticuboctahedron. 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. It is enumerated as the twenty-seventh Johnson solid
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The rectified cubic honeycomb can be dissected and rebuilt as a space-filling lattice oftriangular orthobicupolae and square pyramids.[1]
The dual of the triangular orthobicupola is the trapezo-rhombic dodecahedron. It has 6 rhombic and 6 trapezoidal faces, and is similar to the rhombic dodecahedron.