Digonal-square tetraswirlprism

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Digonal-square tetraswirlprism
File:Digonal-square tetraswirlprism.png
Rank4
TypeIsogonal
Elements
Cells32+32+32 phyllic disphenoids, 16 rhombic disphenoids, 8 square gyroprisms
Faces64+64+64+64 scalene triangles, 8 squares
Edges16+32+32+32+32+32
Vertices32
Vertex figure11-vertex polyhedron with 2 tetragons and 14 triangles
Measures (based on square prisms of edge length 1)
Edge lengthsSide edge 1 (32):
 Side edge 2 (32):
 Side edge 3 (32):
 Side edge 4 (32):
 Digon edges (16): 1
 Edges of squares (32): 1
Circumradius
Central density1
Related polytopes
DualDigonal-square tetraswirltegum
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
Symmetry(I2(8)×I2(16))+/4, order 64
ConvexYes
NatureTame

The digonal-square tetraswirlprism, also known as the 16-2 double step prism or 16-6 double step prism, is a convex isogonal polychoron and member of the duoprismatic swirlprism family that consists of 8 square gyroprisms, 16 rhombic disphenoids, and 96 phyllic disphenoids of three kinds. 2 square gyroprisms, 2 rhombic disphenoids, and 12 phyllic disphenoids joined at each vertex. It can be obtained as a subsymmetrical faceting of the octagonal-hexadecagonal duoprism.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:2.11968.

Vertex coordinates[edit | edit source]

Coordinates for the vertices of a digonal-square tetraswirlprism, assuming that the edge length differences are minimized, are given as Cartesian products of the vertices of square S1 and digon D2 with length ratio 1:1:

  • S1 × D2,
  • S3 × D4 (S1 rotated 22.5 degrees and D2 rotated 45 degrees),
  • S5 × D6 (S1 rotated 45 degrees and D2 rotated 90 degrees),
  • S7 × D8 (S1 rotated 67.5 degrees and D2 rotated 135 degrees).