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.
|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|
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 figuresEdit
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.
- Klitzing, Richard. "trirp".