Truncated cubic prism
Truncated cubic prism  

Rank  4 
Type  Uniform 
Notation  
Bowers style acronym  Ticcup 
Coxeter diagram  x x4x3o () 
Elements  
Cells  8 triangular prisms, 6 octagonal prisms, 2 truncated cubes 
Faces  16 triangles, 12+24 squares, 12 octagons 
Edges  24+24+48 
Vertices  48 
Vertex figure  Sphenoid, edge lengths 1, √2+√2, √2+√2 (base), √2 (legs) 
Measures (edge length 1)  
Circumradius  
Hypervolume  
Dichoral angles  Trip–4–op: 
Op–4–op: 90°  
Tic–8–op: 90°  
Tic–3–trip: 90°  
Height  1 
Central density  1 
Number of external pieces  16 
Level of complexity  12 
Related polytopes  
Army  Ticcup 
Regiment  Ticcup 
Dual  Triakis octahedral tegum 
Conjugate  Quasitruncated hexahedral prism 
Abstract & topological properties  
Flag count  1152 
Euler characteristic  0 
Orientable  Yes 
Properties  
Symmetry  B_{3}×A_{1}, order 96 
Convex  Yes 
Nature  Tame 
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 K4.99 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 crosssections

Segmentochoron display, tic atop tic

Net
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 (BC_{2}×A_{1} axial, octagonal prismfirst)
External links[edit  edit source]
 Bowers, Jonathan. "Category 19: Prisms" (#899).
 Klitzing, Richard. "Ticcup".
 Wikipedia contributors. "Truncated cubic prism".