# Great 10-3 double step prism

Great 10-3 double step prism
Rank4
TypeIsogonal
SpaceSpherical
Elements
Cells10 tetragonal disphenoids, 20 phyllic disphenoids, 40+40 irregular tetrahedra
Faces20 isosceles triangles, 40+40+40+40+40 scalene triangles
Edges10+20+20+40+40
Vertices20
Vertex figure13-vertex polyhedron with 22 triangular faces
Measures (edge length 1)
Central density1
Related polytopes
DualGreat 10-3 bigyrochoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryI2(10)+×4×I, order 40
ConvexYes
NatureTame

The great 10-3 double step prism is a convex isogonal polychoron that consists of 10 tetragonal disphenoids, 20 phyllic disphenoids, and 80 irregular tetrahedra of two kinds. 2 tetragonal disphenoids, 4 phyllic disphenoids, and 16 irregular tetrahedra join at each vertex. I t can be obtained as one of several polychora formed as the convex hull of two orthogonal 10-3 step prisms.

This polychoron cannot be optimized using the ratio method, because the solution (a/b = (3-5)/2) would yield a biambodecachoron instead.

## Vertex coordinates

Coordinates for the vertices of a great 10-3 double step prism are given by:

• (a*sin(2πk/10), a*cos(2πk/10), b*sin(6πk/10), b*cos(6πk/10)),
• (b*sin(2πk/10), b*cos(2πk/10), a*sin(6πk/10), a*cos(6πk/10)),

where a/b is greater than ${\displaystyle \frac{7-3\sqrt5}{2}}$ but less than ${\displaystyle \frac{3-\sqrt5}{2}}$ and k is an integer from 0 to 9.