Great 10-3 double step prism

Great 10-3 double step prism
Rank	4
Type	Isogonal
Space	Spherical
Elements
Cells	10 tetragonal disphenoids, 20 phyllic disphenoids, 40+40 irregular tetrahedra
Faces	20 isosceles triangles, 40+40+40+40+40 scalene triangles
Edges	10+20+20+40+40
Vertices	20
Vertex figure	13-vertex polyhedron with 22 triangular faces
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Great 10-3 bigyrochoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(10)+×4×I, order 40
Convex	Yes
Nature	Tame

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 $\frac{7-3\sqrt5}{2}$ but less than $\frac{3-\sqrt5}{2}$ and k is an integer from 0 to 9.

External links

• Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".