Pentagonal duotransitionalterprism

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Pentagonal duotransitionalterprism
Rank4
TypeIsogonal
Elements
Cells25 rectangular trapezoprisms, 10 pentagonal prisms, 10 pentagonal trapezorhombihedra
Faces100 isosceles trapezoids, 50 rectangles, 25 squares, 20 pentagons
Edges50+100+100
Vertices100
Vertex figureIsosceles trapezoidal pyramid
Measures (edge length 1)
Central density1
Related polytopes
DualPentagonal duotransitionaltertegum
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryH2≀S2, order 200
ConvexYes
NatureTame

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: ≈ 1:2.14412.