Gyrobifastigial 5-2 quadruple step prism

Gyrobifastigial 5-2 quadruple step prism
File:Gyrobifastigial 5-2 quadruple step prism.png (OFF file)
Rank	4
Type	Isogonal
Elements
Cells	10 phyllic disphenoids, 10 wedges, 5 gyrobifastigiums
Faces	20+20 scalene triangles, 5 squares, 20 isosceles trapezoids
Edges	10+10+20+20
Vertices	20
Vertex figure	Digonal-tetragonal gyrowedge
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Elongatotetradisphenoidal intersected 5-2 quadrigyrochoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(5)+×4×I, order 20
Convex	Yes
Nature	Tame

The gyrobifastigial 5-2 quadruple step prism is a convex isogonal polychoron formed as a convex hull of four 5-2 step prisms in a way that leaves eight corealmic vertices corresponding to a gyrobifastigium. It consists of 5 gyrobifastigiums, 10 wedges, and 10 phyllic disphenoids. 2 gyrobifastigiums, 3 wedges, and 2 phyllic disphenoids join at each vertex.

It can be constructed as a diminishing of a uniform small rhombated pentachoron, specifically by removing a gyrochoric-symmetric set of 10 vertices. The wedge cells are the vertex figures of the small rhombated pentachoron. The disphenoids are subsymmetrical facetings of triangular prisms, while the gyrobifastigiums are subsymmetrical facetings of the cuboctahedra. All the original octahedron cells have been reduced to squares only.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:${\sqrt {2}}$ ≈ 1:1.41421.