|Bowers style acronym||Trirp|
|Faces||6 isosceles triangles, 2 triangles|
|Measures (edge lengths 1 (base), a (sides))|
|Dual||Triangular concave antitegum|
|Abstract & topological properties|
|Symmetry||A2×A1, order 12|
The triangular retroprism or trirp, also called the triangular crossed antiprism, is a prismatic isogonal polyhedron. It consists of 2 base triangles and 6 side triangles. The side triangles are isosceles triangles. Each vertex joins one base triangle and three side triangles. It is a crossed antiprism based on a triangle, seen as a 3/2-gon rather than 3/1.
It cannot be made uniform, because if all the edges are of the same length, the height becomes zero and all of the triangles coincide. It can be thought of as a degenerate uniform polyhedron.
It is isomorphic to the octahedron.
In vertex figures[edit | edit source]
Triangular retroprisms occur as vertex figures of seven nonconvex uniform polychora: the faceted rectified pentachoron, faceted rectified tesseract, faceted rectified icositetrachoron, faceted rectified hecatonicosachoron, faceted rectified small stellated hecatonicosachoron, faceted rectified great grand hecatonicosachoron, and faceted rectified great grand stellated hecatonicosachoron.
External links[edit | edit source]
- Klitzing, Richard. "trirp".