Decagonaltruncated cubic duoprism 


Rank  5 

Type  Uniform 

Notation 

Bowers style acronym  Datic 

Coxeter diagram  x10o x4x3o () 

Elements 

Tera  8 triangulardecagonal duoprisms, 10 truncated cubic prisms, 6 octagonaldecagonal duoprisms 

Cells  80 triangular prisms, 60 octagonal prisms, 12+24 decagonal prisms, 10 truncated cubes 

Faces  80 triangles, 120+240 squares, 60 octagons, 24 decagons 

Edges  120+240+240 

Vertices  240 

Vertex figure  Digonal disphenoidal pyramid, edge lengths 1, √2+√2, √2+√2 (base triangle), √(5+√5)/2 (top), √2 (side edges) 

Measures (edge length 1) 

Circumradius  ${\frac {\sqrt {13+4{\sqrt {2}}+2{\sqrt {5}}}}{2}}\approx 2.40463$ 

Hypervolume  $35{\frac {\sqrt {85+60{\sqrt {2}}+34{\sqrt {5}}+24{\sqrt {10}}}}{6}}\approx 104.63865$ 

Diteral angles  Ticcup–tic–ticcup: 144° 

 Tradedip–dip–odedip: $\arccos \left({\frac {\sqrt {3}}{3}}\right)\approx 125.26439^{\circ }$ 

 Tradedip–trip–ticcup: 90° 

 Odedip–op–ticcup: 90° 

 Odedip–dip–odedip: 90° 

Central density  1 

Number of external pieces  24 

Level of complexity  30 

Related polytopes 

Army  Datic 

Regiment  Datic 

Dual  Decagonaltriakis octahedral duotegum 

Conjugates  Decagrammictruncated cubic duoprism, Decagonalquasitruncated hexahedral duoprism, Decagrammicquasitruncated hexahedral duoprism 

Abstract & topological properties 

Euler characteristic  2 

Orientable  Yes 

Properties 

Symmetry  B_{3}×I2(10), order 960 

Convex  Yes 

Nature  Tame 

The decagonaltruncated cubic duoprism or datic is a convex uniform duoprism that consists of 10 truncated cubic prisms, 6 octagonaldecagonal duoprisms, and 8 triangulardecagonal duoprisms. Each vertex joins 2 truncated cubic prisms, 1 triangulardecagonal duoprism, and 2 octagonaldecagonal duoprisms.
The vertices of a triangulartruncated cubic duoprism of edge length 1 are given by all permutations of the last three coordinates of:
 $\left(\pm {\frac {1+{\sqrt {5}}}{2}},\,0,\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1}{2}}\right),$
 $\left(\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\sqrt {\frac {5+{\sqrt {5}}}{8}}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1}{2}}\right),$
 $\left(\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {5+2{\sqrt {5}}}}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1}{2}}\right).$
A decagonaltruncated cubic duoprism has the following Coxeter diagrams:
 x10o x4x3o (full symmetry)
 x5x x4x3o (decagons as dipentagons)