Grünbaum polyhedron
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| Grünbaum polyhedron | |
|---|---|
 | |
| Rank | 3 |
| Type | Isogonal |
| Space | Spherical |
| Elements | |
| Faces | 8+8 equilateral triangles, 24+24 scalene triangles |
| Edges | 24+24+48 |
| Vertices | 24 |
| Measures | |
| Central density | 0 |
| Related polytopes | |
| Army | Snub cube |
| Convex hull | non-uniform snub cube |
| Abstract & topological properties | |
| Flag count | 384 |
| Euler characteristic | –8 |
| Schläfli type | {3,8} |
| Orientable | Yes |
| Genus | 5 |
| Properties | |
| Symmetry | B3+, order 24 |
| Convex | No |
The Grünbaum polyhedron is a realization of the Fricke-Klein map in 3-dimensional Euclidean space with the maximum possible symmetry. The Fricke-Klein map is regular, and thus the Grünbaum polyhedron is regular under its automorphism group, however it is not regular under its symmetry group.
Construction[edit | edit source]
The Grünbaum polyhedron can be constructed by blending two non-identical snub cubes with coincident vertices. The inner snub cube is the same as the outer snub cube with each of its square faces rotated about its own center a quarter turn. If a uniform snub cube is used the inner snub cube will self-intersect. Typically a non-uniform version is used to avoid this.
Gallery[edit | edit source]
External links[edit | edit source]
- Hartley, Michael. "{3,8}*384".