Dodecagonalsmall rhombicuboctahedral duoprism 


Rank  5 

Type  Uniform 

Notation 

Bowers style acronym  Twasirco 

Coxeter diagram  x12o x4o3x () 

Elements 

Tera  8 triangulardodecagonal duoprisms, 6+12 squaredodecagonal duoprisms, 12 small rhombicuboctahedral prisms 

Cells  96 triangular prisms, 72+144 cubes, 24+24 dodecagonal prisms, 12 small rhombicuboctahedra 

Faces  96 triangles, 72+144+288+288 squares, 24 dodecagons 

Edges  288+288+288 

Vertices  288 

Vertex figure  Isoscelestrapezoidal scalene, edge lengths 1, √2, √2, √2 (base trapezoid), √2+√3 (top), √2 (side edges) 

Measures (edge length 1) 

Circumradius  ${\frac {\sqrt {13+2{\sqrt {2}}+4{\sqrt {3}}}}{2}}\approx 2.38520$ 

Hypervolume  $2(12+10{\sqrt {2}}+6{\sqrt {3}}+5{\sqrt {6}})\approx 97.56378$ 

Diteral angles  Sircope–sirco–sircope: 150° 

 Titwadip–twip–sitwadip: $\arccos \left({\frac {\sqrt {6}}{3}}\right)\approx 144.73561^{\circ }$ 

 Sitwadip–twip–sitwadip: 135° 

 Titwadip–trip–sircope: 90° 

 Sitwadip–cube–sircope: 90° 

Central density  1 

Number of external pieces  38 

Level of complexity  40 

Related polytopes 

Army  Twasirco 

Regiment  Twasirco 

Dual  Dodecagonaldeltoidal icositetrahedral duotegum 

Conjugates  Dodecagrammicsmall rhombicuboctahedral duoprism, Dodecagonalquasirhombicuboctahedral duoprism, Dodecagrammicquasirhombicuboctahedral duoprism 

Abstract & topological properties 

Euler characteristic  2 

Orientable  Yes 

Properties 

Symmetry  B_{3}×I_{2}(12), order 1152 

Convex  Yes 

Nature  Tame 

The dodecagonalsmall rhombicuboctahedral duoprism or twasirco is a convex uniform duoprism that consists of 12 small rhombicuboctahedral prisms, 18 squaredodecagonal duoprisms of two kinds, and 8 triangulardodecagonal duoprisms. Each vertex joins 2 small rhombicuboctahedral prisms, 1 triangulardodecagonal duoprism, and 3 squaredodecagonal duoprisms.
This polyteron can be tetrahedrally alternated into a hexagonaltruncated tetrahedral duoalterprism, although it cannot be made scaliform. It can also be tetrahedrally edgesnubbed to create a truncated tetrahedralhexagonal prismalterprismoid, which is also not scaliform.
The vertices of a dodecagonalsmall rhombicuboctahedral duoprism of edge length 1 are given by all permutations of the last three coordinates of:
 $\left(\pm {\frac {1+{\sqrt {3}}}{2}},\,\pm {\frac {1+{\sqrt {3}}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}}\right),$
 $\left(\pm {\frac {1}{2}},\,\pm {\frac {2+{\sqrt {3}}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}}\right),$
 $\left(\pm {\frac {2+{\sqrt {3}}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}}\right).$
A dodecagonalsmall rhombicuboctahedral duoprism has the following Coxeter diagrams:
 x12o x4o3x () (full symmetry)
 x6x x4o3x () (dodecagons as dihexagons)