Square-icosahedral duoprism

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Square-icosahedral duoprism
Rank5
TypeUniform
Notation
Bowers style acronymSquike
Coxeter diagramx4o o5o3x
Elements
Tera20 triangular-square duoprisms, 4 icosahedral prisms
Cells80 triangular prisms, 30 cubes, 4 icosahedra
Faces80 triangles, 12+120 squares
Edges48+120
Vertices48
Vertex figurePentagonal scalene, edge lengths 1 (base pentagon) 2 (top and sides)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesTisdip–cube–tisdip:
 Ipe–ike–ipe: 90°
 Tisdip–trip–ipe: 90°
Height1
Central density1
Number of external pieces24
Level of complexity10
Related polytopes
ArmySquike
RegimentSquike
DualSquare-dodecahedral duotegum
ConjugateSquare-great icosahedral duoprism
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryH3×B2, order 960
ConvexYes
NatureTame

The square-icosahedral duoprism or squike is a convex uniform duoprism that consists of 4 icosahedral prisms and 20 triangular-square duoprisms. Each vertex joins 2 icosahedral prisms and 5 triangular-square duoprisms. It is a duoprism based on a square and an icosahedron, which makes it a convex segmentoteron.

Vertex coordinates[edit | edit source]

The vertices of a square-icosahedral duoprism of edge length 1 are given by all even permutations of the last three coordinates of:

Representations[edit | edit source]

A square-icosahedral duoprism has the following Coxeter diagrams:

  • x4o o5o3x (full symmetry)
  • x x o5o3x (icosahedral prismatic prism)

External links[edit | edit source]