Digonal-scalenohedral 8-3 double step prism
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|Digonal-scalenohedral 8-3 double step prism|
|File:Digonal-scalenohedral 8-3 double step prism.png|
|Cells||16 phyllic disphenoids, 16 tetragonal disphenoids, 8 chiral digonal scalenohedra|
|Faces||32 scalene triangles, 32+32 isosceles triangles|
|Vertex figure||9-vertex polyhedron with 3 tetragons and 8 triangles|
|Measures (based on unit rectified tesseract)|
|Edge lengths||6-valence (16): 1|
|Dual||Trapezoprismatic intersected 8-3 bigyrochoron|
|Abstract & topological properties|
|Symmetry||S2(I2(8)-3)×2R, order 32|
The digonal-scalenohedral 8-3 double step prism is a convex isogonal polychoron, formed as a convex hull of two 8-3 step prisms in a way that leaves six corealmic vertices corresponding to a digonal scalenohedron. It consists of 8 chiral digonal scalenohedra, 16 tetragonal disphenoids, and 16 phyllic disphenoids. 3 digonal scalenohedra, 4 tetragonal disphenoids, and 4 phyllic disphenoids join at each vertex.
It can be constructed by removing an inscribed digonal-scalenohedral 8-3 double step prism from a rectified tesseract.
The ratio between the longest and shortest edges is 1: ≈ 1:1.73205.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of a digonal-scalenohedral 8-3 double step prism are given by:
- (a*sin(2πk/8), a*cos(2πk/8), b*sin(6πk/8), b*cos(6πk/8)),
- (b*sin(2πk/8), b*cos(2πk/8), a*sin(6πk/8), a*cos(6πk/8)),
where a = , b = , and k is an integer from 0 to 7.
External links[edit | edit source]
- Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".