Editing 24-cell (section)

=== Related 4-polytopes ===
Several [[uniform 4-polytope]]s can be derived from the 24-cell via [[Truncation (geometry)|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 [[Regular icosahedron|icosahedron]], or "[[Regular icosahedron#Uniform colorings and subsymmetries|snub octahedron]]."

The 24-cell is the unique convex self-dual regular Euclidean polytope that is neither a [[polygon]] nor a [[simplex (geometry)|simplex]]. Relaxing the condition of convexity admits two further figures: the [[great 120-cell]] and [[grand stellated 120-cell]]. With itself, it can form a [[polytope compound]]: the [[#Symmetries, root systems, and tessellations|compound of two 24-cells]].