# Decagonal-small rhombicuboctahedral duoprism

Decagonal-small rhombicuboctahedral duoprism
Rank5
TypeUniform
Notation
Bowers style acronymDasirco
Coxeter diagramx10o x4o3x ()
Elements
Tera8 triangular-decagonal duoprisms, 6+12 square-decagonal duoprisms, 10 small rhombicuboctahedral prisms
Cells80 triangular prisms, 60+120 cubes, 24+24 decagonal prisms, 10 small rhombicuboctahedra
Faces80 triangles, 60+120+240+240 squares, 24 decagons
Edges240+240+240
Vertices240
Vertex figureIsosceles-trapezoidal scalene, edge lengths 1, 2, 2, 2 (base trapezoid), (5+5)/2 (top), 2 (side edges)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {11+2{\sqrt {2}}+2{\sqrt {5}}}}{2}}\approx 2.13896}$
Hypervolume${\displaystyle 5{\frac {\sqrt {430+300{\sqrt {2}}+172{\sqrt {5}}+120{\sqrt {10}}}}{3}}\approx 67.04768}$
Diteral anglesTradedip–dip–squadedip: ${\displaystyle \arccos \left(-{\frac {\sqrt {6}}{3}}\right)\approx 144.73561^{\circ }}$
Sircope–sirco–sircope: 144°
Central density1
Number of external pieces36
Level of complexity40
Related polytopes
ArmyDasirco
RegimentDasirco
DualDecagonal-deltoidal icositetrahedral duotegum
ConjugatesDecagrammic-small rhombicuboctahedral duoprism, Decagonal-quasirhombicuboctahedral duoprism, Decagrammic-quasirhombicuboctahedral duoprism
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryB3×I2(10), order 960
ConvexYes
NatureTame

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:

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

## Representations

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

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