Triangular-truncated cubic duoprism

Triangular-truncated cubic duoprism
(OFF file)
Rank	5
Type	Uniform
Notation
Bowers style acronym	Tratic
Coxeter diagram	x3o x4x3o ()
Elements
Tera	8 triangular duoprisms, 6 triangular-octagonal duoprisms, 3 truncated cubic prisms
Cells	12+24+24 triangular prisms, 18 octagonal prisms, 3 truncated cubes
Faces	24+24 triangles, 36+72 squares, 18 octagons
Edges	36+72+72
Vertices	72
Vertex figure	Digonal disphenoidal pyramid, edge lengths 1, √2+√2, √2+√2 (base triangle), 1 (top), √2 (side edges)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {25+12{\sqrt {2}}}{12}}}\approx 1.87017$
Hypervolume	$7{\frac {3{\sqrt {3}}+2{\sqrt {6}}}{12}}\approx 5.88883$
Diteral angles	Triddip–trip–todip: $\arccos \left(-{\frac {\sqrt {3}}{3}}\right)\approx 125.26439^{\circ }$
	Triddip–trip–ticcup: 90°
	Todip–op–ticcup: 90°
	Todip–trip–todip: 90°
	Ticcup–tic–ticcup: 60°
Height	${\frac {\sqrt {3}}{2}}\approx 0.86603$
Central density	1
Number of external pieces	17
Level of complexity	30
Related polytopes
Army	Tratic
Regiment	Tratic
Dual	Triangular-triakis octahedral duotegum
Conjugate	Triangular-quasitruncated hexahedral duoprism
Abstract & topological properties
Flag count	8640
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	B3×A2, order 288
Convex	Yes
Nature	Tame

The triangular-truncated cubic duoprism or tratic is a convex uniform duoprism that consists of 3 truncated cubic prisms, 6 triangular-octagonal duoprisms, and 8 triangular duoprisms. Each vertex joins 2 truncated cubic prisms, 1 triangular duoprism, and 2 triangular-octagonal duoprisms. It is a duoprism based on a triangle and a truncated cube, which makes it a convex segmentoteron.

Vertex coordinates

The vertices of a triangular-truncated cubic duoprism of edge length 1 are given by all permutations of the last three coordinates of:

• $\left(0,\,{\frac {\sqrt {3}}{3}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1}{2}}\right),$
• $\left(\pm {\frac {1}{2}},\,-{\frac {\sqrt {3}}{6}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1}{2}}\right).$

External links

• Klitzing, Richard. "tratic".