Cantellated 24-cell

In geometry, the cantellated 24-cell is a uniform polychoron.The boundary of the Cantellated 24-cell is composed of24 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.

Construction

When the cantellation process is applied to 24-cell,each of the 24 octahedra becomes a small rhombicuboctahedron.In addition however, since each octahedra's edge was previously shared with twoother octahedra, the separating edges form the three parallel 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.

tructure

The 24 small rhombicuboctahedrons are joined to each other via their hexagonal faces. The triangular faces of 96 triangular prism are joined to the triangular faces of cuboctahedra.

Gallery

ee also

* Uniform polychoron

External links

* [http://members.aol.com/Polycell/section3.html 3. Convex uniform polychora based on the icositetrachoron (24-cell)] - Model 25