Hendecagonal-small rhombicosidodecahedral duoprism

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Hendecagonal-small rhombicosidodecahedral duoprism
Rank5
TypeUniform
Notation
Bowers style acronymHensrid
Coxeter diagramx11o x5o3x ()
Elements
Tera20 triangular-hendecagonal duoprisms, 30 square-hendecagonal duoprisms, 12 pentagonal-hendecagonal duoprisms, 11 small rhombicosidodecahedral prisms
Cells220 triangular prisms, 330 cubes, 132 pentagonal prisms, 60+60 hendecagonal prisms, 11 small rhombicosidodecahedra
Faces220 triangles, 330+660+660 squares, 132 pentagons, 60 hendecagons
Edges660+660+660
Vertices660
Vertex figureIsosceles-trapezoidal scalene, edge lengths 1, 2, (1+5)/2, 2 (base trapezoid), 2cos(π/11) (top), 2 (side edges)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesThendip–henp–shendip:
 Shendip–henp–pahendip:
 Sriddip–srid–sriddip:
 Thendip–trip–sriddip: 90°
 Shendip–cube–sriddip: 90°
 Pahendip–pip–sriddip: 90°
Central density1
Number of external pieces73
Level of complexity40
Related polytopes
ArmyHensrid
RegimentHensrid
DualHendecagonal-deltoidal hexecontahedral duotegum
ConjugatesSmall hendecagrammic-small rhombicosidodecahedral duoprism, Hendecagrammic-small rhombicosidodecahedral duoprism, Great hendecagrammic-small rhombicosidodecahedral duoprism, Grand hendecagrammic-small rhombicosidodecahedral duoprism, Hendecagonal-quasirhombicosidodecahedral duoprism, Small hendecagrammic-quasirhombicosidodecahedral duoprism, Hendecagrammic-quasirhombicosidodecahedral duoprism, Great hendecagrammic-quasirhombicosidodecahedral duoprism, Grand hendecagrammic-quasirhombicosidodecahedral duoprism
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryH3×I2(11), order 2640
ConvexYes
NatureTame

The hendecagonal-small rhombicosidodecahedral duoprism or hensrid is a convex uniform duoprism that consists of 11 small rhombicosidodecahedral prisms, 12 pentagonal-hendecagonal duoprisms, 30 square-hendecagonal duoprisms, and 20 triangular-hendecagonal duoprisms. Each vertex joins 2 small rhombicosidodecahedral prisms, 1 triangular-hendecagonal duoprism, 2 square-hendecagonal duoprisms, and 1 pentagonal-hendecagonal duoprism.

Vertex coordinates[edit | edit source]

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

as well as all even permutations of the last three coordinates of:

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

External links[edit | edit source]

Klitzing, Richard. "n-srid-dip".