14-4 step prism
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|14-4 step prism|
|Cells||14+14+14 phyllic disphenoids, 7 rhombic disphenoids|
|Faces||28+28+28 scalene triangles, 14 isosceles triangles|
|Vertex figure||9-vertex polyhedron with 14 triangular faces|
|Measures (circumradius , based on a uniform duoprism)|
|Edge lengths||6-valence (14):|
|4-valence (7): 2|
|Abstract & topological properties|
|Symmetry||S2(I2(14)-4), order 28|
The 14-4 step prism is a convex isogonal polychoron and a member of the step prism family. It has 7 rhombic disphenoids and 42 phyllic disphenoids of three kinds as cells, with 14 (2 rhombic and 12 phyllic disphenoids) joining at each vertex.
Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.34899.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of a 14-4 step prism inscribed in a tetradecagonal duoprism with base lengths a and b are given by:
- (a*sin(πk/7), a*cos(πk/7), b*sin(3πk/7), b*cos(3πk/7)),
where k is an integer from 0 to 13. If the edge length differences are to be minimized, the ratio of a:b must be equivalent to 1: ≈ 1:0.92414.
External links[edit | edit source]
- Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".