# Hendecagonal-truncated cubic duoprism

Hendecagonal-truncated cubic duoprism
Rank5
TypeUniform
Notation
Bowers style acronymHentic
Coxeter diagramx11o x4x3o
Elements
Tera8 triangular-hendecagonal duoprisms, 11 truncated cubic prisms, 6 octagonal-hendecagonal duoprisms
Cells88 triangular prisms, 66 octagonal prisms, 12+24 hendecagonal prisms, 11[truncated cubic prism]]s
Faces88 triangles, 132+264 squares, 66 octagons, 24 hendecagons
Edges132+264+264
Vertices264
Vertex figureDigonal disphenoidal pyramid, edge lengths 1, 2+2, 2+2 (base triangle), 2cos(π/11) (top), 2 (side edges)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {7+4{\sqrt {2}}+{\frac {1}{\sin ^{2}{\frac {\pi }{11}}}}}}{2}}\approx 2.51275}$
Hypervolume${\displaystyle {\frac {77(3+2{\sqrt {2}})}{12\tan {\frac {\pi }{11}}}}\approx 127.36955}$
Diteral anglesTiccup–tic–ticcup: ${\displaystyle {\frac {9\pi }{11}}\approx 147.27273^{\circ }}$
Thendip–henp–ohendip: ${\displaystyle \arccos \left(-{\frac {\sqrt {3}}{3}}\right)\approx 125.26439^{\circ }}$
Thendip–trip–ticcup: 90°
Ohendip–op–ticcup: 90°
Ohendip–henp–ohendip: 90°
Central density1
Number of external pieces25
Level of complexity30
Related polytopes
ArmyHentic
RegimentHentic
DualHendecagonal-triakis octahedral duotegum
ConjugatesSmall hendecagrammic-truncated cubic duoprism, Hendecagrammic-truncated cubic duoprism, Great hendecagrammic-truncated cubic duoprism, Grand hendecagrammic-truncated cubic duoprism, Hendecagonal-quasitruncated hexahedral duoprism, Small hendecagrammic-quasitruncated hexahedral duoprism, Hendecagrammic-quasitruncated hexahedral duoprism, Great hendecagrammic-quasitruncated hexahedral duoprism, Grand hendecagrammic-quasitruncated hexahedral duoprism
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryB3×I2(11), order 1056
ConvexYes
NatureTame

The hendecagonal-truncated cubic duoprism or hentic is a convex uniform duoprism that consists of 11 truncated cubic prisms, 6 octagonal-hendecagonal duoprisms, and 8 triangular-hendecagonal duoprisms. Each vertex joins 2 truncated cubic prisms, 1 triangular-hendecagonal duoprism, and 2 octagonal-hendecagonal duoprisms.

## Vertex coordinates

The vertices of a hendecagonal-truncated cubic duoprism of edge length 2sin(π/11) are given by all permutations of the last three coordinates of:

• ${\displaystyle \left(1,\,0,\,\pm (1+{\sqrt {2}})\sin {\frac {\pi }{11}},\,\pm (1+{\sqrt {2}})\sin {\frac {\pi }{11}},\,\pm \sin {\frac {\pi }{11}}\right),}$
• ${\displaystyle \left(\cos \left({\frac {j\pi }{11}}\right),\,\pm \sin \left({\frac {j\pi }{11}}\right),\,\pm (1+{\sqrt {2}})\sin {\frac {\pi }{11}},\,\pm (1+{\sqrt {2}})\sin {\frac {\pi }{11}},\,\pm \sin {\frac {\pi }{11}}\right),}$

where j = 2, 4, 6, 8, 10.