Cantellated 24-cell
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| Cantellated 24-cell | |
|---|---|
 Schlegel diagram |
|
| Type | Uniform polychoron |
| Cells | 24  (4.6.6) |
| Faces | 192 triangles |
| Edges | 864 |
| Vertices | 288 |
| Vertex figure | - |
| Schläfli symbol | t0,2{3,4,3} |
| Symmetry group | B4, [3,4,3] |
| Properties | convex |
In geometry, the cantellated 24-cell is a uniform polychoron. The boundary of the Cantellated 24-cell is composed of 24 Truncated octahedral cells, 24 Cuboctahedral cells and 96 triangular prisms. Together they have 192 triangular faces, 288 squared faces, 96 hexagonal faces, 864 edges, and 288 vertices.
[edit] Construction
When the cantellation process is applied to 24-cell, each of the 24 octahedra becomes a Truncated octahedron. In addition however, since each octahedra's edge was previously shared with two other octahedra, the separating edges form the three parellel edges of a triangular prism - 96 triangular prisms, since the 24-cell contains 96 edges. Further, since each vertex was previously shared with 12 faces, the vertex would split into 12 (24*12=288) new vertices. Each group of 12 new vertices forms a Cuboctahedron.
[edit] Structure
The 24 Truncated octahedron are joined to each other via their hexagonal faces. The triangular faces of 96 triangular prism are joined to the triangular faces of Cuboctahedrons.
[edit] See also
