Pentagonal duotransitionalterprism

Pentagonal duotransitionalterprism
Rank	4
Type	Isogonal
Space	Spherical
Elements
Cells	25 rectangular trapezoprisms, 10 pentagonal prisms, 10 pentagonal trapezorhombihedra
Faces	100 isosceles trapezoids, 50 rectangles, 25 squares, 20 pentagons
Edges	50+100+100
Vertices	100
Vertex figure	Isosceles trapezoidal pyramid
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Pentagonal duotransitionaltertegum
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H2≀S2, order 200
Convex	Yes
Nature	Tame

The pentagonal duotransitionalterprism is a convex isogonal polychoron and the fourth member of the duotransitionalterprism family. It consists of 10 pentagonal trapezorhombihedra, 10 pentagonal prisms, and 25 rectangular trapezoprisms. 2 pentagonal trapezorhombihedra, 1 pentagonal prism, and 2 rectangular trapezoprisms join at each vertex. It can be obtained as the convex hull of two orthogonal pentagonal-dipentagonal duoprisms. However, it cannot be made scaliform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$\frac{2+\sqrt{3+\sqrt5}}{2}$ ≈ 1:2.14412.