Heawood map
Jump to navigation
Jump to search
| Heawood map | |
|---|---|
 | |
| Rank | 3 |
| Type | Regular map, Regular toroid, Chiral polyhedron |
| Elements | |
| Faces | 7 hexagons |
| Edges | 21 |
| Vertices | 14 |
| Vertex figure | Triangle |
| Petrie polygons | 3 tetradecagons |
| Abstract & topological properties | |
| Flag count | 84 |
| Euler characteristic | 0 |
| Schläfli type | {6,3} |
| Orientable | Yes |
| Genus | 1 |
| Skeleton | Heawood graph |
| Properties | |
| Symmetry | C7⋊C6, order 42 |
| Flag orbits | 2 |
The Heawood map is a regular map. Its automorphism group dart-transitive, thus it is a regular toroid and a regular map. However is not an abstract regular polytope since its automorphism group is not flag-transitive.
With seven hexagonal faces, it has the least number of faces out of any toroid. It also has the unusual property that each of its faces is adjacent to all of the other faces.
It can be realized in 3-dimensional space with planar faces and without self-intersection as the Szilassi polyhedron.
Gallery[edit | edit source]
-
The Heawood map with a hexagonal fundamental polygon
External links[edit | edit source]
- Wedd, N. The Heawood map