Dodecagonaltruncated cubic duoprism 


Rank  5 

Type  Uniform 

Notation 

Bowers style acronym  Twatic 

Coxeter diagram  x12o x4x3o () 

Elements 

Tera  8 triangulardodecagonal duoprisms, 6 hexagonaldodecagonal duoprisms 

Cells  96 triangular prisms, 72 octagonal prisms, 12+24 dodecagonal prisms, 12 truncated cubes 

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

Edges  144+288+288 

Vertices  288 

Vertex figure  Digonal disphenoidal pyramid, edge lengths 1, √2+√2, √2+√2 (base triangle), √2+√3 (top), √2 (side edges) 

Measures (edge length 1) 

Circumradius  ${\frac {\sqrt {15+4{\sqrt {2}}+4{\sqrt {3}}}}{2}}\approx 2.62607$ 

Hypervolume  $7(6+4{\sqrt {2}}+3{\sqrt {3}}+2{\sqrt {6}})\approx 152.26390$ 

Diteral angles  Ticcup–tic–ticcup: 150° 

 Titwadip–twip–otwadip: $\arccos \left({\frac {\sqrt {3}}{3}}\right)\approx 125.26439^{\circ }$ 

 Titwadip–trip–ticcup: 90° 

 Otwadip–op–ticcup: 90° 

 Otwadip–twip–otwadip: 90° 

Central density  1 

Number of external pieces  26 

Level of complexity  30 

Related polytopes 

Army  Twatic 

Regiment  Twatic 

Dual  Dodecagonaltriakis octahedral duotegum 

Conjugates  Dodecagrammictruncated cubic duoprism, Dodecagonalquasitruncated hexahedral duoprism, Dodecagrammicquasitruncated hexahedral duoprism 

Abstract & topological properties 

Euler characteristic  2 

Orientable  Yes 

Properties 

Symmetry  B_{3}×I2(12), order 1152 

Convex  Yes 

Nature  Tame 

The dodecagonaltruncated cubic duoprism or twatic is a convex uniform duoprism that consists of 12 truncated cubic prisms, 6 octagonaldodecagonal duoprisms and 8 triangulardodecagonal duoprisms. Each vertex joins 2 truncated cubic prisms, 1 triangulardodecagonal duoprism, and 2 octagonaldodecagonal duoprisms.
The vertices of a dodecagonaltruncated cubic duoprism of edge length 1 are given by all permutations of the last three coordinates of:
 $\left(\pm {\frac {1+{\sqrt {3}}}{2}},\,\pm {\frac {1+{\sqrt {3}}}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1}{2}}\right),$
 $\left(\pm {\frac {1}{2}},\,\pm {\frac {2+{\sqrt {3}}}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1}{2}}\right),$
 $\left(\pm {\frac {2+{\sqrt {3}}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1}{2}}\right).$
A dodecagonaltruncated cubic duoprism has the following Coxeter diagrams:
 x12o x4x3o () (full symmetry)
 x6x x4x3o () (dodecagons as dihexagons)