18-6 gyrochoron
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18-6 gyrochoron | |
---|---|
Rank | 4 |
Type | Isotopic |
Elements | |
Cells | 18 tetragonal antiwedges |
Faces | 18+18 isosceles triangles, 18 kites |
Edges | 3+18+36 |
Vertices | 3+18 |
Vertex figure | 18 phyllic disphenoids, 3 hexagonal gyrotegums |
Measures (edge length 1) | |
Central density | 1 |
Related polytopes | |
Dual | 18-6 step prism |
Abstract & topological properties | |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | S2(I2(18)-6), order 36 |
Convex | Yes |
Nature | Tame |
The 18-6 gyrochoron, also known as the trigon hexacoil, is a convex isochoric polychoron and member of the gyrochoron family with 18 tetragonal antiwedges as cells.
Each cell of this polychoron has bilateral symmetry, with 2 kites and 4 isosceles triangles for faces.
Isogonal derivatives[edit | edit source]
Substitution by vertices of these following elements will produce these convex isogonal polychora:
- Tetragonal antiwedge (18): 18-6 step prism
- Kite (18): 18-6 step prism
- Isosceles triangle (18): 18-6 step prism
- Edge (18): 18-6 step prism
- Edge (36): 36-6 step prism
- Vertex (18): 18-6 step prism
External links[edit | edit source]
- Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".