Medial 15-4 double step prism

Medial 15-4 double step prism
File:Medial 15-4 double step prism.png (OFF file)
Rank	4
Type	Isogonal
Space	Spherical
Elements
Cells	60 irregular tetrahedra, 30+30+30+30 phyllic disphenoids, 15 rhombic disphenoids
Faces	60+60+60+60+60+60 scalene triangles, 30 isosceles triangles
Edges	15+30+30+30+30+30+60
Vertices	30
Vertex figure	15-vertex polyhedron with 26 triangles
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Medial 15-4 bigyrochoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	S2(I2(15)-4)×2R, order 60
Convex	Yes
Nature	Tame

The medial 15-4 double step prism is a convex isogonal polychoron that consists of 15 rhombic disphenoids, 120 phyllic disphenoids of four kinds, and 60 irregular tetrahedra. 2 rhombic disphenoids, 16 phyllic disphenoids, and 8 irregular tetrahedra join at each vertex. It can be obtained as the convex hull of two orthogonal 15-4 step prisms.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$\frac{\sqrt{979-33\sqrt5+22\sqrt{1590-18\sqrt5}}}{22}$ ≈ 1:1.91303.