Truncated cubic prism

Truncated cubic prism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
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	$\sqrt{2+\sqrt2} ≈ 1.84776$
Hypervolume	$7\frac{3+2\sqrt2}{3} ≈ 13.59966$
Dichoral angles	Trip–4–op: $\arccos\left(-\frac{\sqrt3}{3}\right) ≈ 125.26439°$
	Op–4–op: 90°
	Tic–8–op: 90°
	Tic–3–trip: 90°
Height	1
Central density	1
Number of pieces	16
Level of complexity	12
Related polytopes
Army	Ticcup
Regiment	Ticcup
Dual	Triakis octahedral tegum
Conjugate	Quasitruncated hexahedral prism
Abstract properties
Flag count	1152
Euler characteristic	0
Topological properties
Orientable	Yes
Properties
Symmetry	B3×A1, order 96
Convex	Yes
Nature	Tame
Discovered by	{{{discoverer}}}

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

• 

  Card with cell counts, verf, and cross-sections

• 

  Segmentochoron display, tic atop tic

• 

  Net

Vertex coordinates

The vertices of a truncated cubic prism of edge length 1 are given by all permutations of the first three coordinates of:

• $\left(±\frac{1+\sqrt2}{2},\,±\frac{1+\sqrt2}{2},\,±\frac12,\,±\frac12\right).$

Representations

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

• Bowers, Jonathan. "Category 19: Prisms" (#899).

• Klitzing, Richard. "Ticcup".

• Wikipedia Contributors. "Truncated cubic prism".