# Square duotransitionalterprism

Square duotransitionalterprism
File:Square duotransitionalterprism.png
Rank4
TypeIsogonal
Elements
Cells16 rectangular trapezoprisms, 8 square prisms, 8 square trapezorhombihedra
Faces64 isosceles trapezoids, 32 rectangles, 16+16 squares
Edges32+64+64
Vertices64
Vertex figureIsosceles trapezoidal pyramid
Measures (edge length 1)
Central density1
Related polytopes
DualSquare duotransitionaltertegum
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryB2≀S2, order 128
ConvexYes
NatureTame

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

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:

• ${\displaystyle \left(\pm 1,\,\pm 1,\,\pm {\frac {1}{2}},\,\pm {\frac {3}{2}}\right),}$
• ${\displaystyle \left(\pm 1,\,\pm 1,\,\pm {\frac {3}{2}},\,\pm {\frac {1}{2}}\right),}$
• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {3}{2}},\,\pm 1,\,\pm 1\right),}$
• ${\displaystyle \left(\pm {\frac {3}{2}},\,\pm {\frac {1}{2}},\,\pm 1,\,\pm 1\right).}$