Hendecagonal-small rhombicuboctahedral duoprism

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Hendecagonal-small rhombicuboctahedral duoprism
Rank5
TypeUniform
Notation
Bowers style acronymHensirco
Coxeter diagramx11o x4o3x
Elements
Tera8 triangular-hendecagonal duoprisms, 6+12 square-hendecagonal duoprisms
Cells88 triangular prisms, 66+132 cubes, 24+24 hendecagonal prisms, 11 small rhombicuboctahedra
Faces88 triangles, 66+132+264+264 squares, 24 hendecagon
Edges264+264+264
Vertices264
Vertex figureIsosceles-trapezoidal scalene, edge lengths 1, 2, 2, 2 (base trapezoid), 2cos(π/11) (top), 2 (side edges)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesSircope–sirco–sircope:
 Thendip–henp–shendip:
 Shendip–henp–shendip: 135°
 Thendip–trip–sircope: 90°
 Shendip–cube–sircope: 90°
Central density1
Number of external pieces37
Level of complexity40
Related polytopes
ArmyHensirco
RegimentHensirco
DualHendecagonal-deltoidal icositetrahedral duotegum
ConjugatesSmall hendecagrammic-small rhombicuboctahedral duoprism, Hendecagrammic-small rhombicuboctahedral duoprism, Great hendecagrammic-small rhombicuboctahedral duoprism, Grand hendecagrammic-small rhombicuboctahedral duoprism, Hendecagonal-quasirhombicuboctahedral duoprism, Small hendecagrammic-quasirhombicuboctahedral duoprism, Hendecagrammic-quasirhombicuboctahedral duoprism, Great hendecagrammic-quasirhombicuboctahedral duoprism, Grand hendecagrammic-quasirhombicuboctahedral duoprism
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryB3×I2(11), order 1056
ConvexYes
NatureTame

The hendecagonal-small rhombicuboctahedral duoprism or hensirco is a convex uniform duoprism that consists of 11 small rhombicuboctahedral prisms, 18 square-hendecagonal duoprisms of two kinds, and 8 triangular-hendecagonal duoprisms. Each vertex joins 2 small rhombicuboctahedral prisms, 1 triangular-hendecagonal duoprism, and 3 square-hendecagonal duoprisms.

Vertex coordinates[edit | edit source]

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

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