Fricke-Klein map
Jump to navigation
Jump to search
| Fricke-Klein map | |
|---|---|
| Rank | 3 |
| Type | Regular |
| Space | Spherical |
| Elements | |
| Faces | 64 triangles |
| Edges | 96 |
| Vertices | 24 |
| Vertex figure | Octagon |
| Petrie polygons | 16 dodecagons |
| Holes | Octagons |
| Abstract & topological properties | |
| Flag count | 384 |
| Euler characteristic | -8 |
| Schläfli type | {3,8} |
| Orientable | Yes |
| Genus | 5 |
The Fricke-Klein map is a regular map and abstract polyhedron.
Related polytopes[edit | edit source]
- The most symmetric geometric realization of the Fricke-Klein map in 3D space is the Grünbaum polyhedron.
- The Fricke-Klein map is a double cover of the Dyck map.
External links[edit | edit source]
- Hartley, Michael. "{3,8}*384".
Bibliography[edit | edit source]
- Gévay, Gábor; Schulte, Egon; Wills, Jörg (2016). "The Regular Grünbaum Polyhedron of Genus 5". Advances in Geometry. arXiv:1212.6588.
- Schulte, Egon; Wills, Jörg (1987). "Kepler-Poinsot-Type Realizations of Regular Maps of Klein, Fricke, Gordan and Sherk" (PDF). Canadian Math Bulletin. 30.