Heptagonal-small rhombicuboctahedral duoprism

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Heptagonal-small rhombicuboctahedral duoprism
Rank5
TypeUniform
Notation
Bowers style acronymHesirco
Coxeter diagramx7o x4o3x
Elements
Tera8 triangular-heptagonal duoprisms, 6+12 square-heptagonal duoprisms, 7 small rhombicuboctahedral prisms
Cells56 triangular prisms, 42+84 cubes, 24+24 heptagonal prisms, 7 small rhombicuboctahedra
Faces56 triangles, 42+84+168+168 squares, 24 heptagons
Edges168+168+168
Vertices168
Vertex figureIsosceles-trapezoidal scalene, edge lengths 1, 2, 2, 2 (base trapezoid), 2cos(π/7) (top), 2 (side edges)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesTheddip–hep–squahedip:
 Squahedip–hep–squahedip: 135°
 Sircope–sirco–sircope:
 Theddip–trip–sircope: 90°
 Squahedip–cube–sircope: 90°
Central density1
Number of external pieces33
Level of complexity40
Related polytopes
ArmyHesirco
RegimentHesirco
DualHeptagonal-deltoidal icositetrahedral duotegum
ConjugatesHeptagrammic-small rhombicuboctahedral duoprism, Great heptagrammic-small rhombicuboctahedral duoprism, Heptagonal-quasirhombicuboctahedral duoprism, Heptagrammic-quasirhombicuboctahedral duoprism, Great heptagrammic-quasirhombicuboctahedral duoprism
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryB3×I2(7), order 672
ConvexYes
NatureTame

The heptagonal-small rhombicuboctahedral duoprism or hesirco is a convex uniform duoprism that consists of 7 small rhombicuboctahedral prisms, 18 square-heptagonal duoprisms of two kinds, and 8 triangular-heptagonal duoprisms. Each vertex joins 2 small rhombicuboctahedral prisms, 1 triangular-heptagonal duoprism, and 3 square-heptagonal duoprisms.

Vertex coordinates[edit | edit source]

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

where j = 2, 4, 6.