In four-dimensional geometry, the 24-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {3,4,3}. It is also called C₂₄, or the icositetrachoron, octaplex (short for "octahedral complex"), icosatetrahedroid, octacube, hyper-diamond or polyoctahedron, being constructed of octahedral cells.

The boundary of the 24-cell is composed of 24 octahedral cells with six meeting at each vertex, and three at each edge. Together they have 96 triangular faces, 96 edges, and 24 vertices. The vertex figure is a cube. The 24-cell is self-dual. The 24-cell and the tesseract are the only convex regular 4-polytopes in which the edge length equals the radius.

The 24-cell does not have a regular analogue in three dimensions or any other number of dimensions, either below or above. It is the only one of the six convex regular 4-polytopes which is not the analogue of one of the five Platonic solids. However, it can be seen as the analogue of a pair of irregular solids: the cuboctahedron and its dual the rhombic dodecahedron.

Translated copies of the 24-cell can tesselate four-dimensional space face-to-face, forming the 24-cell honeycomb. As a polytope that can tile by translation, the 24-cell is an example of a parallelotope, the simplest one that is not also a zonotope.

The 24-cell incorporates the geometries of every convex regular polytope in the first four dimensions, except the 5-cell, those with a 5 in their Schlӓfli symbol, and the regular polygons with 7 or more sides. In other words, the 24-cell contains all of the regular polytopes made of triangles and squares that exist in four dimensions except the regular 5-cell, but none of the pentagonal polytopes. The geometric relationships among all of these regular polytopes can be observed in a single 24-cell or the 24-cell honeycomb.

The 24-cell is the fourth in the sequence of six convex regular 4-polytopes (in order of size and complexity). It can be deconstructed into 3 overlapping instances of its predecessor the tesseract (8-cell), as the 8-cell can be deconstructed into 2 instances of its predecessor the 16-cell. The reverse procedure to construct each of these from an instance of its predecessor preserves the radius of the predecessor, but generally produces a successor with a smaller edge length.

The 24-cell has two natural systems of Cartesian coordinates, which reveal distinct structure.

The 24-cell is the convex hull of its vertices which can be described as the 24 coordinate permutations of: