Hendecagonal-great rhombicosidodecahedral duoprism

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Hendecagonal-great rhombicosidodecahedral duoprism
Rank5
TypeUniform
Notation
Bowers style acronymHengrid
Coxeter diagramx11o x5x3x
Elements
Tera30 square-hendecagonal duoprisms, 20 hexagonal-hendecagonal duoprisms, 12 decagonal-hendecagonal duoprisms, 11 great rhombicosidodecahedral prisms
Cells330 cubes, 220 hexagonal prisms, 132 decagonal prisms, 60+60+60 hendecagonal prisms, 11 great rhombicosidodecahedra
Faces330+660+660+660 squares, 220 hexagons, 132 decagons, 120 hendecagons
Edges660+660+660+1320
Vertices1320
Vertex figureMirror-symmetric pentachoron, edge lengths 2, 3, (5+5)/2 (base triangle), 2cos(π/11) (top edge), 2 (side edges)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesShendip–henp–hahendip:
 Shendip–henp–dahendip:
 Griddip–grid–griddip:
 Hahendip–henp–dahendip:
 Shendip–cube–griddip: 90°
 Hahendip–hip–griddip: 90°
 Dahendip–dip–griddip: 90°
Central density1
Number of external pieces73
Level of complexity60
Related polytopes
ArmyHengrid
RegimentHengrid
DualHendecagonal-disdyakis triacontahedral duotegum
ConjugatesSmall hendecagrammic-great rhombicosidodecahedral duoprism, Hendecagrammic-great rhombicosidodecahedral duoprism, Great hendecagrammic-great rhombicosidodecahedral duoprism, Grand hendecagrammic-great rhombicosidodecahedral duoprism, Hendecagonal-great quasitruncated icosidodecahedral duoprism, Small hendecagrammic-great quasitruncated icosidodecahedral duoprism, Hendecagrammic-great quasitruncated icosidodecahedral duoprism, Great hendecagrammic-great quasitruncated icosidodecahedral duoprism, Grand hendecagrammic-great quasitruncated icosidodecahedral duoprism
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryH3×I2(11), order 2640
ConvexYes
NatureTame

The hendecagonal-great rhombicosidodecahedral duoprism or hengrid is a convex uniform duoprism that consists of 11 great rhombicosidodecahedral prisms, 12 decagonal-hendecagonal duoprisms, 20 hexagonal-hendecagonal duoprisms, and 30 square-hendecagonal duoprisms. Each vertex joins 2 great rhombicosidodecahedral prisms, 1 square-hendecagonal duoprism, 1 hexagonal-hendecagonal duoprism, and 1 decagonal-hendecagonal duoprism.

Vertex coordinates[edit | edit source]

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

along with all even permutations of the last three coordinates of:

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