Truncated cubic prism
|Truncated cubic prism|
|Bowers style acronym||Ticcup|
|Coxeter diagram||x x4x3o ()|
|Cells||8 triangular prisms, 6 octagonal prisms, 2 truncated cubes|
|Faces||16 triangles, 12+24 squares, 12 octagons|
|Vertex figure||Sphenoid, edge lengths 1, √2+√2, √2+√2 (base), √2 (legs)|
|Measures (edge length 1)|
|Number of pieces||16|
|Level of complexity||12|
|Dual||Triakis octahedral tegum|
|Conjugate||Quasitruncated hexahedral prism|
|Symmetry||B3×A1, order 96|
The truncated cubic prism or ticcup, is a prismatic uniform polychoron that consists of 2 truncated cubes, 6 octagonal prisms, and 8 triangular prisms. Each vertex joins 1 truncated cube, 1 octagonal prism, and 2 triangular prisms. As the name suggests, it is a prism based on the truncated cube. As such it is also a convex segmentochoron (designated K-4.99 on Richard Klitzing's list).
The truncated cubic prism can be obtained from a small rhombated tesseract by removing two small rhombicuboctahedron atop truncated cube segmentochora. This diminishing cuts the lateral small rhombicuboctahedra into their equatorial octagonal prisms only. It is also a central segment of the small prismatotetracontoctachoron.
Gallery[edit | edit source]
Card with cell counts, verf, and cross-sections
Segmentochoron display, tic atop tic
Vertex coordinates[edit | edit source]
The vertices of a truncated cubic prism of edge length 1 are given by all permutations of the first three coordinates of:
Representations[edit | edit source]
The truncated cubic prism has the following Coxeter diagrams:
- x x4x3o (full symmetry)
- xx4xx3oo&#x (bases considered separately)
- xxxx xwwx4xoox&#xt (BC2×A1 axial, octagonal prism-first)
External links[edit | edit source]
- Bowers, Jonathan. "Category 19: Prisms" (#899).
- Klitzing, Richard. "Ticcup".
- Wikipedia Contributors. "Truncated cubic prism".