Small 10-3 double step prism
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|Small 10-3 double step prism|
|File:Small 10-3 double step prism.png|
|Cells||10 tetragonal disphenoids, 20+20 phyllic disphenoids, 40 irregular tetrahedra|
|Faces||20 isosceles triangles, 40+40+40+40 scalene triangles|
|Vertex figure||11-vertex polyhedron with 18 triangular faces|
|Measures (edge length 1)|
|Dual||Small 10-3 bigyrochoron|
|Abstract & topological properties|
|Symmetry||I2(10)+×4×I, order 40|
The small 10-3 double step prism is a convex isogonal polychoron that consists of 10 tetragonal disphenoids, 40 phyllic disphenoids of two kinds, and 40 irregular tetrahedra. 2 tetragonal disphenoids, 8 phyllic disphenoids, and 8 irregular tetrahedra join at each vertex. It 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 would yield a biambodecachoron instead.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of a small 10-3 double step prism are given by:
where a/b is greater than but less than 1, and k is an integer from 0 to 9.
External links[edit | edit source]
- Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".