Császár polyhedron
In geometry, the Császár polyhedron (Hungarian: [ˈt͡ʃaːsaːr]) is a nonconvex toroidal polyhedron with 14 triangular faces.
| Császár polyhedron | |
|---|---|
An animation of the Császár polyhedron being rotated and unfolded | |
| Type | Toroidal polyhedron |
| Faces | 14 triangles |
| Edges | 21 |
| Vertices | 7 |
| Euler char. | 0 (Genus 1) |
| Vertex configuration | 3.3.3.3.3.3 |
| Symmetry group | C1, [ ]+, (11) |
| Dual polyhedron | Szilassi polyhedron |
| Properties | Non-convex |
This polyhedron has no diagonals; every pair of vertices is connected by an edge. The seven vertices and 21 edges of the Császár polyhedron form an embedding of the complete graph K7 onto a topological torus. Of the 35 possible triangles from vertices of the polyhedron, only 14 are faces.
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