Cube (simplex realization)
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| Cube (simplex realization) | |
|---|---|
| Rank | 3 |
| Dimension | 7 |
| Type | Regular |
| Notation | |
| Schläfli symbol | {4,3}#{}#{3,3}π |
| Elements | |
| Faces | 6 skew squares |
| Edges | 12 |
| Vertices | 8 |
| Vertex figure | Triangle |
| Petrie polygons | 4 skew hexagonal-triangular coils |
| Related polytopes | |
| Army | Oca |
| Petrie dual | Petrial cube (simplex realization) |
| Convex hull | 7-simplex |
| Abstract & topological properties | |
| Flag count | 48 |
| Schläfli type | {4,3} |
| Orientable | Yes |
| Properties | |
| Flag orbits | 1 |
| Convex | No |
| Dimension vector | (3,5,5) |
The simplex realization of {4,3} is a regular skew polyhedron in 7-dimensional Euclidean space. It can be constructed as the blend of the Petrial tetrahedron, the convex cube, and a dyad.
Vertex coordinates[edit | edit source]
The vertex coordinates of the simplex realization of {4,3} are the same as the those of the 7-simplex.
Related polytopes[edit | edit source]
: Faithful realization
: Non-faithful realization
: Blend with the convex cube.
: Blend with the Petrial tetrahedron.
: Blend with the dyad.
The simplex realization of the cube is one of 5 faithful symmetric realizations of the abstract polyhedron {4,3}.
External links[edit | edit source]
- Hartley, Michael. "{4,3}*48".
- Wedd, N. The cube