8-2 step prism
|8-2 step prism|
|Cells||8+8 phyllic disphenoids, 4 rhombic disphenoids|
|Faces||16+16 scalene triangles, 8 isosceles triangles|
|Vertex figure||Ridge-triakis notch|
|Measures (circumradius , based on a uniform duoprism)|
|Edge lengths||6-valence (8):|
|4-valence (4): 2|
|Abstract & topological properties|
|Symmetry||S2(I2(8)-2), order 16|
The 8-2 step prism is a convex isogonal polychoron and a member of the step prism family. It has 4 rhombic disphenoids and 16 phyllic disphenoids of two kinds as cells, with a total of 10 (2 rhombic and 8 phyllic disphenoids) joining at each vertex. It is one of 3 isogonal polychora with 8 vertices, and the only one not to be uniform (the other 2 are the hexadecachoron and tetrahedral prism).
Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.48563.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of an 8-2 step prism inscribed in an octagonal duoprism with base lengths a and b are given by:
- (a*sin(πk/4), a*cos(πk/4), b*sin(πk/2), b*cos(πk/2)),
where k is an integer from 0 to 7. If the edge length differences are to be minimized, the ratio of a:b must be equivalent to 1: ≈ 1:1.30656.
Isogonal derivatives[edit | edit source]
Substitution by vertices of these following elements will produce these convex isogonal polychora:
- Phyllic disphenoid (8): 8-2 step prism
- Scalene triangle (8): 8-2 step prism
- Scalene triangle (16): 16-2 step prism
- Edge (8): 8-2 step prism
External links[edit | edit source]
- Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".