Square duotransitionalterprism

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Square duotransitionalterprism
File:Square duotransitionalterprism.png
Cells16 rectangular trapezoprisms, 8 square prisms, 8 square trapezorhombihedra
Faces64 isosceles trapezoids, 32 rectangles, 16+16 squares
Vertex figureIsosceles trapezoidal pyramid
Measures (edge length 1)
Central density1
Related polytopes
DualSquare duotransitionaltertegum
Abstract & topological properties
Euler characteristic0
SymmetryB2≀S2, order 128

The square duotransitionalterprism is a convex isogonal polychoron and the third member of the duotransitionalterprism family. It consists of 8 square trapezorhombihedra, 8 square prisms, and 16 rectangular trapezoprisms. 2 square trapezorhombihedra, 1 square prism, and 2 rectangular trapezoprisms join at each vertex. It can be obtained as the convex hull of two orthogonal square-ditetragonal duoprisms. However, it cannot be made scaliform.

This polychoron can be alternated into a digonal duotransitionalterantiprism, which is also not scaliform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:2.

Vertex coordinates[edit | edit source]

The vertices of a square duotransitionalterprism, assuming that the isosceles trapezoids have three equal edges of length 1, centered at the origin, are given by: