25-7 step prism
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|25-7 step prism|
|File:25-7 step prism.png|
|Cells||50+50 phyllic disphenoids, 25 tetragonal disphenoids|
|Faces||100 scalene triangles, 50+100 isosceles triangles|
|Vertex figure||Paratetraaugmented snub disphenoid|
|Measures (circumradius , based on a uniform duoprism)|
|Edge lengths||6-valence (50):|
|Abstract & topological properties|
|Symmetry||S2(I2(25)-7)×2I, order 100|
The 25-7 step prism is a convex isogonal polychoron, member of the step prism family. It has 25 tetragonal disphenoids and 100 phyllic disphenoids of two kinds as cells with 20 (4 tetragonal and 16 phyllic disphenoids) meeting at each vertex.
Compared to other 25-vertex step prisms, this polychoron has doubled symmetry, because 25 is a factor of 72+1 = 50.
The ratio between the longest and shortest edges is 1: ≈ 1:1.67124.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of a 25-7 step prism of circumradius √2 are given by:
- (sin(2πk/25), cos(2πk/25), sin(14πk/25), cos(14πk/25)),
where k is an integer from 0 to 24.