# Triangular-small rhombicuboctahedral duoprism

Triangular-small rhombicuboctahedral duoprism
Rank5
TypeUniform
Notation
Bowers style acronymTrasirco
Coxeter diagramx3o x4o3x ()
Elements
Tera8 triangular duoprisms, 6+12 triangular-square duoprisms, 3 small rhombicuboctahedral prisms
Cells24+24+24 triangular prisms, 18+36 cubes, 3 small rhombicuboctahedra
Faces24+24 triangles, 18+36+72+72 squares
Edges72+72+72
Vertices72
Vertex figureIsosceles-trapezoidal scalene, edge lengths 1, 2, 2, 2 (base trapezoid), 1 (top), 2 (side edges)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {19+6{\sqrt {2}}}{12}}}\approx 1.51342}$
Hypervolume${\displaystyle {\frac {6{\sqrt {3}}+5{\sqrt {6}}}{6}}\approx 3.77329}$
Diteral anglesTriddip–trip–tisdip: ${\displaystyle \arccos \left(-{\frac {\sqrt {6}}{3}}\right)\approx 144.73561^{\circ }}$
Tisdip–trip–tisdip: 135°
Triddip–trip–sircope: 90°
Tisdip–cube–sircope: 90°
Sircope–sirco–sircope: 60°
Height${\displaystyle {\frac {\sqrt {3}}{2}}\approx 0.86603}$
Central density1
Number of external pieces29
Level of complexity40
Related polytopes
ArmyTrasirco
RegimentTrasirco
DualTriangular-deltoidal icositetrahedral duotegum
ConjugateTriangular-quasirhombicuboctahedral duoprism
Abstract & topological properties
Flag count11520
Euler characteristic2
OrientableYes
Properties
SymmetryB3×A2, order 288
ConvexYes
NatureTame

The triangular-small rhombicuboctahedral duoprism or trasirco is a convex uniform duoprism that consists of 3 small rhombicuboctahedral prisms, 18 triangular-square duoprisms, of two kinds and 8 triangular duoprisms. Each vertex joins 2 small rhombicuboctahedral prisms, 1 triangular duoprism, and 3 triangular-square duoprisms. It is a duoprism based on a triangle and a small rhombicuboctahedron, which makes it a convex segmentoteron.

## Vertex coordinates

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

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