7-2 step prismatic alterprism

7-2 step prismatic alterprism
File:7-2 step prismatic alterprism.png (OFF file)
Rank	5
Type	Isogonal
Elements
Tera	14+14+14 bilaterally-symmetric pentachora, 14 bilaterally-symmetric triangular duotegums, 2 7-2 step prisms
Cells	28+28+28 irregular tetrahedra, 14+14+14+14+14+14+14 phyllic disphenoids
Faces	28+28+28+28+28 scalene triangles, 14+14+14+14 isosceles triangles
Edges	14+14+14+14+14+14
Vertices	14
Vertex figure	12-vertex polychoron with 22 tetrahedra
Measures (edge length 1)
Central density	1
Related polytopes
Dual	7-2 gyrochoric altertegum
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	(S2(I2(14)-3)×A1)/2, order 28
Convex	Yes
Nature	Tame

The 7-2 step prismatic alterprism is a convex isogonal polyteron that consists of 2 7-2 step prisms, 14 bilaterally-symmetric triangular duotegums, and 42 bilaterally-symmetric pentachora of three kinds. 1 7-2 step prism, 6 bilaterally-symmetric triangular duotegums, and 15 bilaterally-symmetric pentachora join at each vertex. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:${\sqrt {2\cos {\frac {\pi }{7}}}}$ ≈ 1:1.34236.