Medial 13-5 double step prism

Medial 13-5 double step prism
File:Medial 13-5 double step prism.png
Rank	4
Type	Isogonal
Elements
Cells	13 tetragonal disphenoids, 26 phyllic disphenoids, 52+52 irregular tetrahedra
Faces	26+52 isosceles triangles, 52+52+52+52 scalene triangles
Edges	13+26+26+52+52
Vertices	26
Vertex figure	13-vertex polyhedron with 22 triangular faces
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Medial 13-5 bigyrochoron
Abstract & topological properties
Flag count	3432
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	S2(I2(13)-5)×2I, order 52
Convex	Yes
Nature	Tame

The medial 13-5 double step prism is a convex isogonal polychoron that consists of 13 tetragonal disphenoids, 26 phyllic disphenoids, and 104 irregular tetrahedra of two kinds. 2 tetragonal disphenoids, 4 phyllic disphenoids, and 16 irregular tetrahedra join at each vertex. It can be obtained as the convex hull of two orthogonal 13-5 step prisms.

This polychoron cannot be optimized using the ratio method, because the solution ${\frac {a}{b}}={\frac {2+{\sqrt {4+2\cos \left({\frac {\pi }{13}}\right)+2\sin \left({\frac {3\pi }{26}}\right)}}}{2\cos \left({\frac {2\pi }{13}}\right)}}$ would yield a small 13-5 double step prism instead.