Heptagonal-truncated dodecahedral duoprism

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Heptagonal-truncated dodecahedral duoprism
Rank5
TypeUniform
Notation
Bowers style acronymHetid
Coxeter diagramx7o x5x3o
Elements
Tera20 triangular-heptagonal duoprisms, 12 heptagonal-decagonal duoprisms, 7 truncated dodecahedral prisms
Cells140 triangular prisms, 30+60 heptagonal prisms, 84 decagonal prisms, 7 truncated dodecahedra
Faces140 triangles, 210+420 squares, 60 heptagons, 84 decagons
Edges210+420+420
Vertices420
Vertex figureDigonal disphenoidal pyramid, edge lengths 1, (5+5)/2, (5+5)/2 (base triangle), cos(π/7) (top), 2 (side edges)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesTheddip–hep–hedadip:
 Tiddip–tid–tiddip:
 Hedadip–hep–hedadip:
 Theddip–trip–tiddip: 90°
 Hedadip–dip–tiddip: 90°
Central density1
Number of external pieces39
Level of complexity30
Related polytopes
ArmyHetid
RegimentHetid
DualHeptagonal-triakis icosahedral duotegum
ConjugatesHeptagrammic-truncated dodecahedral duoprism, Great heptagrammic-truncated dodecahedral duoprism, Heptagonal-quasitruncated great stellated dodecahedral duoprism, Heptagrammic-quasitruncated great stellated dodecahedral duoprism, Great heptagrammic-quasitruncated great stellated dodecahedral duoprism
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryH3×I2(7), order 1680
ConvexYes
NatureTame

The heptagonal-truncated dodecahedral duoprism or hetid is a convex uniform duoprism that consists of 7 truncated dodecahedral prisms, 12 heptagonal-decagonal duoprisms, and 20 triangular-heptagonal duoprisms. Each vertex joins 2 truncated dodecahedral prisms, 1 triangular-heptagonal duoprism, and 2 heptagonal-decagonal duoprisms.

Vertex coordinates[edit | edit source]

The vertices of a heptagonal-truncated dodecahedral duoprism of edge length 2sin(π/7) are given by all even permutations of the last three coordinates of:

where j = 2, 4, 6.