Császár polyhedron
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| Császár polyhedron | |
|---|---|
 | |
| Rank | 3 |
| Type | Regular toroid |
| Space | Spherical |
| Elements | |
| Faces | 2+2+2+2+2+2+2 scalene triangles |
| Edges | 1+1+1+2+2+2+2+2+2+2+2+2 |
| Vertices | 1+2+2+2 |
| Vertex figure | 2+2+2 irregular hexagons, 1 bilaterally-symmetric hexagon |
| Related polytopes | |
| Dual | Szilassi polyhedron |
| Abstract & topological properties | |
| Euler characteristic | 0 |
| Orientable | Yes |
| Genus | 1 |
| Properties | |
| Symmetry | K2+×I, order 2 |
| Convex | No |
| History | |
| Discovered by | Ákos Császár |
| First discovered | 1949 |
The Császár polyhedron (Hungarian: [ˈt͡ʃaːsaːr], approximate English pronunciation CHA-sar) is a toroidal polyhedron without any diagonals; that is, every pair of vertices is connected by an edge. It is the dual of the Szilassi polyhedron. It is a regular toroid, but it is not abstractly regular.
It has 14 scalene triangular faces, 7 vertices, and 21 edges. 6 faces meet at each vertex.
Its vertices and edges are an embedding of the complete graph K7 onto a torus of genus 1.
It has the same edge skeleton as the 7-2 step prism.
External links[edit | edit source]
- Wikipedia Contributors. "Császár polyhedron".
- McCooey, David. "Csaszar Polyhedron"