10-3 double gyrostep prism
|10-3 double gyrostep prism|
|Symmetry||I2(10)+×4×I, order 40|
|Cells||10+10 tetragonal disphenoids, 20 phyllic disphenoids, 40 irregular tetrahedra|
|Faces||20+20 isosceles triangles, 40+40+40 scalene triangles|
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 = (√-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 √-2 but less than (√-1)/2 and k is an integer from 0 to 9.
[edit | edit source]
- Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".
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