7-2 gyrochoron
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| 7-2 gyrochoron | |
|---|---|
 | |
| Rank | 4 |
| Type | Isotopic |
| Elements | |
| Cells | 7 bilaterally-symmetric edge-truncated tetrahedra |
| Faces | 7 isosceles triangles, 7 kites, 7 mirror-symmetric pentagons |
| Edges | 7+7+14 |
| Vertices | 7+7 |
| Vertex figure | 7+7 phyllic disphenoids |
| Measures (edge length 1) | |
| Central density | 1 |
| Related polytopes | |
| Dual | 7-2 step prism |
| Abstract & topological properties | |
| Flag count | 336 |
| Euler characteristic | 0 |
| Orientable | Yes |
| Properties | |
| Symmetry | S2(I2(7)-2), order 14 |
| Flag orbits | 24 |
| Convex | Yes |
| Nature | Tame |
The 7-2 gyrochoron, also known as möbius 7, is a convex isotopic polychoron and member of the gyrochoron family with 7 bilaterally-symmetric edge-truncated tetrahedra as cells. It is the simplest gyrochoron after the pentachoron and triangular duoprism, both members of existing families, as well as the only isochoric polychoron with 7 cells. It can also be constructed as the 7-3 gyrochoron. It is also the triangular funk prism.
Each cell of this polychoron has bilateral symmetry, with 2 mirror-symmetric pentagons, 2 kites, and 2 isosceles triangles for faces, and shares a face with every other cell.
Gallery[edit | edit source]
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Wireframe, cell, net
Isogonal derivatives[edit | edit source]
Substitution by vertices of these following elements will produce these convex isogonal polychora:
- Edge-truncated tetrahedron (7): 7-2 step prism
- Mirror-symmetric pentagon (7): 7-2 step prism
- Kite (7): 7-2 step prism
- Isosceles triangle (7): 7-2 step prism
- Edge (7): 7-2 step prism
- Edge (14): 14-2 step prism
- Vertex (7): 7-2 step prism
External links[edit | edit source]
- Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".