# Triangular-truncated cubic duoprism

Triangular-truncated cubic duoprism
Rank5
TypeUniform
Notation
Bowers style acronymTratic
Coxeter diagramx3o x4x3o ()
Elements
Tera8 triangular duoprisms, 6 triangular-octagonal duoprisms, 3 truncated cubic prisms
Cells12+24+24 triangular prisms, 18 octagonal prisms, 3 truncated cubes
Faces24+24 triangles, 36+72 squares, 18 octagons
Edges36+72+72
Vertices72
Vertex figureDigonal disphenoidal pyramid, edge lengths 1, 2+2, 2+2 (base triangle), 1 (top), 2 (side edges)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {25+12{\sqrt {2}}}{12}}}\approx 1.87017}$
Hypervolume${\displaystyle 7{\frac {3{\sqrt {3}}+2{\sqrt {6}}}{12}}\approx 5.88883}$
Diteral anglesTriddip–trip–todip: ${\displaystyle \arccos \left(-{\frac {\sqrt {3}}{3}}\right)\approx 125.26439^{\circ }}$
Triddip–trip–ticcup: 90°
Todip–op–ticcup: 90°
Todip–trip–todip: 90°
Ticcup–tic–ticcup: 60°
Height${\displaystyle {\frac {\sqrt {3}}{2}}\approx 0.86603}$
Central density1
Number of external pieces17
Level of complexity30
Related polytopes
ArmyTratic
RegimentTratic
DualTriangular-triakis octahedral duotegum
ConjugateTriangular-quasitruncated hexahedral duoprism
Abstract & topological properties
Flag count8640
Euler characteristic2
OrientableYes
Properties
SymmetryB3×A2, order 288
ConvexYes
NatureTame

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:

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