10-3 double gyrostep prism

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10-3 double gyrostep prism
Rank4
TypeIsogonal
SpaceSpherical
Info
SymmetryI2(10)+×4×I, order 40
Elements
Cells10+10 tetragonal disphenoids, 20 phyllic disphenoids, 40 irregular tetrahedra
Faces20+20 isosceles triangles, 40+40+40 scalene triangles
Edges20+20+20+40
Vertices20
Central density1
Euler characteristic0
Related polytopes
Dual10-3 antibigyrochoron
Properties
ConvexYes
OrientableYes
NatureTame

The 10-3 double gyrostep prism is a convex isogonal polychoron that consists of 20 tetragonal disphenoids of two kinds, 20 phyllic disphenoids and 40 irregular tetrahedra obtained 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 = (5-1)/2) would yield a small prismatodecachoron instead.

Vertex coordinates[edit | edit source]

Coordinates for the vertices of a 10-3 double gyrostep 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 5-2 but less than (5-1)/2 and k is an integer from 0 to 9.

External links[edit | edit source]