# Digonal-scalenohedral 8-3 double step prism

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Digonal-scalenohedral 8-3 double step prism
File:Digonal-scalenohedral 8-3 double step prism.png
Rank4
TypeIsogonal
SpaceSpherical
Elements
Cells16 phyllic disphenoids, 16 tetragonal disphenoids, 8 chiral digonal scalenohedra
Faces32 scalene triangles, 32+32 isosceles triangles
Edges8+16+16+32
Vertices16
Vertex figure9-vertex polyhedron with 3 tetragons and 8 triangles
Measures (based on unit rectified tesseract)
Edge lengths6-valence (16): 1
4-valence (16): ${\displaystyle \sqrt2 ≈ 1.41421}$
4-valence (8): ${\displaystyle \sqrt3 ≈ 1.73205}$
3-valence (32): ${\displaystyle \sqrt3 ≈ 1.73205}$
Circumradius${\displaystyle \frac{\sqrt6}{2} ≈ 1.22475}$
Central density1
Related polytopes
DualTrapezoprismatic intersected 8-3 bigyrochoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryS2(I2(8)-3)×2R, order 32
ConvexYes
NatureTame

The digonal-scalenohedral 8-3 double step prism is a convex isogonal polychoron, formed as a convex hull of two 8-3 step prisms in a way that leaves six corealmic vertices corresponding to a digonal scalenohedron. It consists of 8 chiral digonal scalenohedra, 16 tetragonal disphenoids, and 16 phyllic disphenoids. 3 digonal scalenohedra, 4 tetragonal disphenoids, and 4 phyllic disphenoids join at each vertex.

It can be constructed by removing an inscribed digonal-scalenohedral 8-3 double step prism from a rectified tesseract.

The ratio between the longest and shortest edges is 1:${\displaystyle \sqrt3}$ ≈ 1:1.73205.

## Vertex coordinates

Coordinates for the vertices of a digonal-scalenohedral 8-3 double step prism are given by:

• (a*sin(2πk/8), a*cos(2πk/8), b*sin(6πk/8), b*cos(6πk/8)),
• (b*sin(2πk/8), b*cos(2πk/8), a*sin(6πk/8), a*cos(6πk/8)),

where a = ${\displaystyle \frac{\sqrt2-1}{2}}$, b = ${\displaystyle \frac{1+\sqrt2}{2}}$, and k is an integer from 0 to 7.