# 24-7 step prism

24-7 step prism Rank4
TypeIsogonal
SpaceSpherical
Elements
Cells48+48 phyllic disphenoids, 24 rhombic disphenoids
Faces96+96 scalene triangles, 48 isosceles triangles
Edges24+24+48+48
Vertices24
Vertex figureParatetraaugmented hexagonal tegum
Measures (circumradius $\sqrt2$ , based on a uniform duoprism)
Edge lengths8-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 density1
Related polytopes
Dual24-7 gyrochoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryS2(I2(24)-7)×2R, order 96
ConvexYes
NatureTame

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.