24-cell - Related 4-polytopes

Related 4-polytopes

Several uniform polychora can be derived from the 24-cell via truncation:

• truncating at 1/3 of the edge length yields the truncated 24-cell;
• truncating at 1/2 of the edge length yields the rectified 24-cell;
• and truncating at half the depth to the dual 24-cell yields the bitruncated 24-cell, which is cell-transitive.

The 96 edges of the 24-cell can be partitioned into the golden ratio to produce the 96 vertices of the snub 24-cell. This is done by first placing vectors along the 24-cell's edges such that each two-dimensional face is bounded by a cycle, then similarly partitioning each edge into the golden ratio along the direction of its vector. An analogous modification to an octahedron produces an icosahedron, or "snub octahedron."