Decagonal-small rhombicuboctahedral duoprism

Decagonal-small rhombicuboctahedral duoprism
(OFF file)
Rank	5
Type	Uniform
Notation
Bowers style acronym	Dasirco
Coxeter diagram	x10o x4o3x ()
Elements
Tera	8 triangular-decagonal duoprisms, 6+12 square-decagonal duoprisms, 10 small rhombicuboctahedral prisms
Cells	80 triangular prisms, 60+120 cubes, 24+24 decagonal prisms, 10 small rhombicuboctahedra
Faces	80 triangles, 60+120+240+240 squares, 24 decagons
Edges	240+240+240
Vertices	240
Vertex figure	Isosceles-trapezoidal scalene, edge lengths 1, √2, √2, √2 (base trapezoid), √(5+√5)/2 (top), √2 (side edges)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {11+2{\sqrt {2}}+2{\sqrt {5}}}}{2}}\approx 2.13896$
Hypervolume	$5{\frac {\sqrt {430+300{\sqrt {2}}+172{\sqrt {5}}+120{\sqrt {10}}}}{3}}\approx 67.04768$
Diteral angles	Tradedip–dip–squadedip: $\arccos \left(-{\frac {\sqrt {6}}{3}}\right)\approx 144.73561^{\circ }$
	Sircope–sirco–sircope: 144°
	Squadedip–dip–squadedip: 135°
	Tradedip–trip–sircope: 90°
	Squadedip–cube–sircope: 90°
Central density	1
Number of external pieces	36
Level of complexity	40
Related polytopes
Army	Dasirco
Regiment	Dasirco
Dual	Decagonal-deltoidal icositetrahedral duotegum
Conjugates	Decagrammic-small rhombicuboctahedral duoprism, Decagonal-quasirhombicuboctahedral duoprism, Decagrammic-quasirhombicuboctahedral duoprism
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	B3×I2(10), order 960
Convex	Yes
Nature	Tame

The decagonal-small rhombicuboctahedral duoprism or dasirco is a convex uniform duoprism that consists of 10 small rhombicuboctahedral prisms, 18 square-decagonal duoprisms of two kinds, and 8 triangular-decagonal duoprisms. Each vertex joins 2 small rhombicuboctahedral prisms, 1 triangular-decagonal duoprism, and 3 square-decagonal duoprisms.

This polychoron can be tetrahedrally alternated into a pentagonal-truncated tetrahedral duoalterprism, although it cannot be made scaliform.

Vertex coordinates

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

• $\left(0,\,\pm {\frac {1+{\sqrt {5}}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}}\right),$
• $\left(\pm {\sqrt {\frac {5+{\sqrt {5}}}{8}}},\,\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}}\right),$
• $\left(\pm {\frac {\sqrt {5+2{\sqrt {5}}}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}}\right).$

Representations

A decagonal-small rhombicuboctahedral duoprism has the following Coxeter diagrams:

• x10o x4o3x () (full symmetry)
• x5x o4x3o () (decagons as dipentagons)