Truncated cubic prism

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Truncated cubic prism
Rank4
TypeUniform
Notation
Bowers style acronymTiccup
Coxeter diagramx x4x3o ()
Elements
Cells8 triangular prisms, 6 octagonal prisms, 2 truncated cubes
Faces16 triangles, 12+24 squares, 12 octagons
Edges24+24+48
Vertices48
Vertex figureSphenoid, edge lengths 1, 2+2, 2+2 (base), 2 (legs)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesTrip–4–op:
 Op–4–op: 90°
 Tic–8–op: 90°
 Tic–3–trip: 90°
Height1
Central density1
Number of external pieces16
Level of complexity12
Related polytopes
ArmyTiccup
RegimentTiccup
DualTriakis octahedral tegum
ConjugateQuasitruncated hexahedral prism
Abstract & topological properties
Flag count1152
Euler characteristic0
OrientableYes
Properties
SymmetryB3×A1, order 96
ConvexYes
NatureTame

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]

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]