Triangular-small rhombicuboctahedral duoprism

Triangular-small rhombicuboctahedral duoprism
(OFF file)
Rank	5
Type	Uniform
Notation
Bowers style acronym	Trasirco
Coxeter diagram	x3o x4o3x ()
Elements
Tera	8 triangular duoprisms, 6+12 triangular-square duoprisms, 3 small rhombicuboctahedral prisms
Cells	24+24+24 triangular prisms, 18+36 cubes, 3 small rhombicuboctahedra
Faces	24+24 triangles, 18+36+72+72 squares
Edges	72+72+72
Vertices	72
Vertex figure	Isosceles-trapezoidal scalene, edge lengths 1, √2, √2, √2 (base trapezoid), 1 (top), √2 (side edges)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {19+6{\sqrt {2}}}{12}}}\approx 1.51342$
Hypervolume	${\frac {6{\sqrt {3}}+5{\sqrt {6}}}{6}}\approx 3.77329$
Diteral angles	Triddip–trip–tisdip: $\arccos \left(-{\frac {\sqrt {6}}{3}}\right)\approx 144.73561^{\circ }$
	Tisdip–trip–tisdip: 135°
	Triddip–trip–sircope: 90°
	Tisdip–cube–sircope: 90°
	Sircope–sirco–sircope: 60°
Height	${\frac {\sqrt {3}}{2}}\approx 0.86603$
Central density	1
Number of external pieces	29
Level of complexity	40
Related polytopes
Army	Trasirco
Regiment	Trasirco
Dual	Triangular-deltoidal icositetrahedral duotegum
Conjugate	Triangular-quasirhombicuboctahedral duoprism
Abstract & topological properties
Flag count	11520
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	B3×A2, order 288
Convex	Yes
Nature	Tame

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:

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

External links

• Klitzing, Richard. "trasirco".