Square duotransitionalterprism

Square duotransitionalterprism
File:Square duotransitionalterprism.png (OFF file)
Rank	4
Type	Isogonal
Space	Spherical
Elements
Cells	16 rectangular trapezoprisms, 8 square prisms, 8 square trapezorhombihedra
Faces	64 isosceles trapezoids, 32 rectangles, 16+16 squares
Edges	32+64+64
Vertices	64
Vertex figure	Isosceles trapezoidal pyramid
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Square duotransitionaltertegum
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B2≀S2, order 128
Convex	Yes
Nature	Tame

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:

• $\left(±1,\,±1,\,±\frac12,\,±\frac32\right),$
• $\left(±1,\,±1,\,±\frac32,\,±\frac12\right),$
• $\left(±\frac12,\,±\frac32,\,±1,\,±1\right),$
• $\left(±\frac32,\,±\frac12,\,±1,\,±1\right).$