Digonal-square tetraswirlprism

(Redirected from 16-6 double step prism)
Digonal-square tetraswirlprism
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Rank4
TypeIsogonal
SpaceSpherical
Info
SymmetryI2(8)×I2(16)/8, order 64
Elements
Cells8 square antiprisms, 16 rhombic disphenoids, 32+32+32 phyllic disphenoids
Faces8 squares, 64+64+64+64 scalene triangles
Edges16+32+32+32+32+32
Vertices32
Central density1
Euler characteristic0
Related polytopes
DualDigonal-square tetraswirltegum
Properties
ConvexYes
OrientableYes
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 that consists of 8 square antiprisms, 16 rhombic disphenoids and 96 phyllic disphenoids of three kinds 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:${\displaystyle \frac{\sqrt{14356+6402\sqrt2+388\sqrt{1186+833\sqrt2}}}{97}}$ ≈ 1:2.11968.

Vertex coordinates

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).