Hendecagonal-snub cubic duoprism

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Hendecagonal-snub cubic duoprism
Rank5
TypeUniform
Notation
Bowers style acronymHensnic
Coxeter diagramx11o s4s3s
Elements
Tera8+24 triangular-hendecagonal duoprisms, 6 square-hendecagonal duoprisms, 11 snub cubic prisms
Cells88+264 triangular prisms, 66 cubes, 12+24+24 hendecagonal prisms, 11 snub cubes
Faces88+264 triangles, 66+132+264+264 squares, 24 hendecagons
Edges132+264+264+264
Vertices264
Vertex figureMirror-symmetric pentagonal scalene, edge lengths 1, 1, 1, 1, 2 (base pentagon), 2cos(π/11) (top edge), 2 (side edges)
Measures (edge length 1)
Circumradius≈ 2.22604
Hypervolume≈ 73.89003
Diteral anglesThendip–henp–thendip: ≈ 153.23459°
 Sniccup–snic–sniccup:
 Thendip–henp–shendip: ≈ 142.98343°
 Thendip–trip–sniccup: 90°
 Shendip–cube–sniccup: 90°
Central density1
Number of external pieces49
Level of complexity50
Related polytopes
ArmyHensnic
RegimentHensnic
DualHendecagonal-pentagonal icositetrahedral duotegum
ConjugatesSmall hendecagrammic-snub cubic duoprism, Hendecagrammic-snub cubic duoprism, Great hendecagrammic-snub cubic duoprism, Grand hendecagrammic-snub cubic duoprism
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryB3+×I2(11), order 528
ConvexYes
NatureTame

The hendecagonal-snub cubic duoprism or hensnic is a convex uniform duoprism that consists of 11 snub cubic prisms, 6 square-hendecagonal duoprisms, and 32 triangular-hendecagonal duoprisms of two kinds. Each vertex joins 2 snub cubic prisms, 4 triangular-hendecagonal duoprisms, and 1 square-hendecagonal duoprism.

Vertex coordinates[edit | edit source]

The vertices of a hendecagonal-snub cubic duoprism of edge length 2sin(π/11) are given by by all even permutations with an even number of sign changes, plus all odd permutations with an odd amount of sign changes, of the last three coordinates of:

where

  • j = 2, 4, 6, 8, 10,