12-5 double gyrostep prism
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|12-5 double gyrostep prism|
|File:12-5 double gyrostep prism.png|
|Cells||24+24+24 phyllic disphenoids, 48 irregular tetrahedra|
|Faces||24+24 isosceles triangles, 48+48+48+48 scalene triangles|
|Vertex figure||12-vertex polyhedron with 20 triangular faces|
|Measures (edge length 1)|
|Abstract & topological properties|
|Symmetry||I2(12)+×4×I, order 48|
The 12-5 double gyrostep prism is a convex isogonal polychoron that consists of 12 tetragonal disphenoids, 24 rhombic disphenoids of two kinds, 24 phyllic disphenoids and 48 irregular tetrahedra. 12 phyllic disphenoids and 8 irregular tetrahedra join at each vertex. It can be obtained as the convex hull of two orthogonal 12-5 step prisms.
This polychoron cannot be optimized using the ratio method, because the solution (a/b = ) would yield a 24-5 step prism instead.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of a 12-5 double gyrostep prism are given by:
- (a*sin(2πk/12), a*cos(2πk/12), b*sin(10πk/12), b*cos(10πk/12)),
- (b*sin(2πk/12), b*cos(2πk/12), a*sin(10πk/12), a*cos(10πk/12)),
where a/b is greater than √2-√3 but less than 2√3+√14-8√3-3 and k is an integer from 0 to 11.
External links[edit | edit source]
- Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".