# 12-2 step prism

12-2 step prism Rank4
TypeIsogonal
SpaceSpherical
Elements
Cells12+12+12+12 phyllic disphenoids, 6 rhombic disphenoids
Faces24+24+24+24 scalene triangles, 12 isosceles triangles
Edges6+12+12+12+12+12
Vertices12
Vertex figureRidge-tritriakis notch
Measures (circumradius $\sqrt2$ , based on a uniform duoprism)
Edge lengths10-valence (12): $\sqrt{3-\sqrt3} ≈ 1.12603$ 3-valence (12): 2
4-valence (6): 2
4-valence (12): $\sqrt{3+\sqrt3} ≈ 2.17533$ 4-valence (12+12): $\sqrt6 ≈ 2.44949$ Central density1
Related polytopes
Dual12-2 gyrochoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryS2(I2(12)-2), order 24
ConvexYes
NatureTame

The 12-2 step prism is a convex isogonal polychoron and a member of the step prism family. It has 6 rhombic disphenoids and 48 phyllic disphenoids of four kinds as cells, with 18 (2 rhombic and 16 phyllic disphenoids) joining at each vertex.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$\frac{\sqrt{10+4\sqrt3}}{2}$ ≈ 1:2.05719.

## Vertex coordinates

Coordinates for the vertices of a 12-2 step prism inscribed in a dodecagonal duoprism with base lengths a and b are given by:

• (a*sin(πk/6), a*cos(πk/6), b*sin(πk/3), b*cos(πk/3)),

where k is an integer from 0 to 11. If the edge length differences are to be minimized, the ratio of a:b must be equivalent to 1:$\sqrt{2+\sqrt3}$ ≈ 1:1.93185.