Triangular cupolic prism
|Triangular cupolic prism|
|Bowers style acronym||Tricupe|
|Coxeter diagram||xx ox3xx&#x|
|Cells||1+3 triangular prisms, 3 cubes, 2 triangular cupolas, 1 hexagonal prism|
|Faces||2+6 triangles, 3+3+3+6+6 squares, 2 hexagons|
|Vertex figures||6 rectangular pyramids, base edge lengths 1 and √, side edge length √|
|12 irregular tetrahedra, edge lengths 1 (1), √ (4), and √ (1)|
|Measures (edge length 1)|
|Heights||Tricu atop tricu: 1|
|Trip atop hip:|
|Dual||Semibisected hexagonal trapezohedral tegum|
|Abstract & topological properties|
|Symmetry||A2×A1×I, order 12|
The triangular cupolic prism, or tricupe, is a CRF segmentochoron (designated K-4.45 on Richard Klitzing's list). It consists of 2 triangular cupolas, 4 triangular prisms, 3 cubes, and 1 hexagonal prism.
As the name suggests, it is a prism based on the triangular cupola. As such, it is a segmentochoron between two triangular cupolas. It can also be viewed as a segmentochoron between a hexagonal prism and a triangular prism.
Two triangular cupolic prisms can be joined at their hexagonal prismatic cells in opposite orientations to form a cuboctahedral prism. By rotating one of the triangular cupolic prisms before joining, one can instead form a triangular orthobicupolic prism.
Vertex coordinates[edit | edit source]
Coordinates of the vertices of a triangular cupolic prism of edge length 1 centered at the origin are given by:
[edit | edit source]
- Klitzing, Richard. "tricupe".