Decagonalsmall rhombicuboctahedral duoprism 


Rank  5 

Type  Uniform 

Notation 

Bowers style acronym  Dasirco 

Coxeter diagram  x10o x4o3x () 

Elements 

Tera  8 triangulardecagonal duoprisms, 6+12 squaredecagonal 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  Isoscelestrapezoidal 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  Decagonaldeltoidal icositetrahedral duotegum 

Conjugates  Decagrammicsmall rhombicuboctahedral duoprism, Decagonalquasirhombicuboctahedral duoprism, Decagrammicquasirhombicuboctahedral duoprism 

Abstract & topological properties 

Euler characteristic  2 

Orientable  Yes 

Properties 

Symmetry  B_{3}×I_{2}(10), order 960 

Convex  Yes 

Nature  Tame 

The decagonalsmall rhombicuboctahedral duoprism or dasirco is a convex uniform duoprism that consists of 10 small rhombicuboctahedral prisms, 18 squaredecagonal duoprisms of two kinds, and 8 triangulardecagonal duoprisms. Each vertex joins 2 small rhombicuboctahedral prisms, 1 triangulardecagonal duoprism, and 3 squaredecagonal duoprisms.
This polychoron can be tetrahedrally alternated into a pentagonaltruncated tetrahedral duoalterprism, although it cannot be made scaliform.
The vertices of a decagonalsmall rhombicuboctahedral duoprism of edge length 1 are given by all permutations of the last three coordinates of:
 $\left(0,\,\pm {\frac {1+{\sqrt {5}}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}}\right),$
 $\left(\pm {\sqrt {\frac {5+{\sqrt {5}}}{8}}},\,\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}}\right),$
 $\left(\pm {\frac {\sqrt {5+2{\sqrt {5}}}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}}\right).$
A decagonalsmall rhombicuboctahedral duoprism has the following Coxeter diagrams:
 x10o x4o3x () (full symmetry)
 x5x o4x3o () (decagons as dipentagons)