# Dodecagonal-truncated cubic duoprism

Dodecagonal-truncated cubic duoprism
Rank5
TypeUniform
Notation
Bowers style acronymTwatic
Coxeter diagramx12o x4x3o ()
Elements
Tera8 triangular-dodecagonal duoprisms, 6 hexagonal-dodecagonal duoprisms
Cells96 triangular prisms, 72 octagonal prisms, 12+24 dodecagonal prisms, 12 truncated cubes
Faces96 triangles, 144+288 squares, 72 octagons, 24 dodecagons
Edges144+288+288
Vertices288
Vertex figureDigonal disphenoidal pyramid, edge lengths 1, 2+2, 2+2 (base triangle), 2+3 (top), 2 (side edges)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {15+4{\sqrt {2}}+4{\sqrt {3}}}}{2}}\approx 2.62607}$
Hypervolume${\displaystyle 7(6+4{\sqrt {2}}+3{\sqrt {3}}+2{\sqrt {6}})\approx 152.26390}$
Diteral anglesTiccup–tic–ticcup: 150°
Titwadip–twip–otwadip: ${\displaystyle \arccos \left(-{\frac {\sqrt {3}}{3}}\right)\approx 125.26439^{\circ }}$
Central density1
Number of external pieces26
Level of complexity30
Related polytopes
ArmyTwatic
RegimentTwatic
DualDodecagonal-triakis octahedral duotegum
ConjugatesDodecagrammic-truncated cubic duoprism, Dodecagonal-quasitruncated hexahedral duoprism, Dodecagrammic-quasitruncated hexahedral duoprism
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryB3×I2(12), order 1152
ConvexYes
NatureTame

The dodecagonal-truncated cubic duoprism or twatic is a convex uniform duoprism that consists of 12 truncated cubic prisms, 6 octagonal-dodecagonal duoprisms and 8 triangular-dodecagonal duoprisms. Each vertex joins 2 truncated cubic prisms, 1 triangular-dodecagonal duoprism, and 2 octagonal-dodecagonal duoprisms.

## Vertex coordinates

The vertices of a dodecagonal-truncated cubic duoprism of edge length 1 are given by all permutations of the last three coordinates of:

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

## Representations

A dodecagonal-truncated cubic duoprism has the following Coxeter diagrams:

• x12o x4x3o () (full symmetry)
• x6x x4x3o () (dodecagons as dihexagons)