24-7 step prism

24-7 step prism
(OFF file)
Rank	4
Type	Isogonal
Space	Spherical
Elements
Cells	48+48 phyllic disphenoids, 24 rhombic disphenoids
Faces	96+96 scalene triangles, 48 isosceles triangles
Edges	24+24+48+48
Vertices	24
Vertex figure	Paratetraaugmented hexagonal tegum
Measures (circumradius $\sqrt2$, based on a uniform duoprism)
Edge lengths	8-valence (24): $\sqrt{4-2\sqrt2} \approx 1.08239$
	4-valence (24): $\sqrt2 \approx 1.41421$
	6-valence (48): $\sqrt{4-\sqrt2} \approx 1.60804$
	3-valence (48): 2
Central density	1
Related polytopes
Dual	24-7 gyrochoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	S2(I2(24)-7)×2R, order 96
Convex	Yes
Nature	Tame

The 24-7 step prism, also known as the digonal double triswirlprism, is a convex isogonal polychoron and a member of the step prism family. It has 24 rhombic disphenoids and 96 phyllic disphenoids of two kinds as cells, with 20 (4 rhombic and 16 phyllic disphenoids) joining at each vertex. It is the second in an infinite family of isogonal digonal prismatic swirlchora.

The ratio between the longest and shortest edges is 1:$\sqrt{2+\sqrt2}$ ≈ 1:1.84776.

Vertex coordinates

Coordinates for the vertices of a 24-7 step prism of circumradius √2 are given by:

• $\left(\sin\frac{\pi k}{12},\,\cos\frac{\pi k}{12},\,\sin\frac{7\pi k}{12},\,\cos\frac{7\pi k}{12}\right),$

where k is an integer from 0 to 23.