Geometry
The snub 24-cell is related to the truncated 24-cell by an alternation operation. Half the vertices are deleted, the 24 truncated octahedron cells become 24 icosahedron cells, the 24 cubes become 24 tetrahedron cells, and the 96 deleted vertex voids create 96 new tetrahedron cells.
A net of the snub 24-cell with blue icosahedra, and red and yellow tetrahedra. |
The snub 24-cell may also be constructed by a particular diminishing of the 600-cell: by removing 24 vertices from the 600-cell corresponding to those of an inscribed 24-cell, and then taking the convex hull of the remaining vertices. This is equivalent to removing 24 icosahedral pyramids from the 600-cell.
Conversely, the 600-cell may be constructed from the snub 24-cell by augmenting it with 24 icosahedral pyramids.
Read more about this topic: Snub 24-cell
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