The four-dimensional regular polytope made of 24 octahedral cells is the 24-cell.
A 24-cell is the four-dimensional analogue of a Platonic solid. Its boundary consists of 24 regular octahedra, which are called cells because they occupy the three-dimensional boundary of a four-dimensional object. The polytope has 24 vertices, 96 edges, and 96 triangular faces; six octahedral cells meet at every vertex.
Its Schläfli symbol is {3,4,3}. This records the structure: triangular faces form the octahedral cells, four triangles meet at each octahedron vertex, and the vertex figure of the whole polytope is a cube. Unlike most regular polytopes, the 24-cell is self-dual, meaning its vertices and cells correspond in the dual structure.
The 24-cell is easy to confuse with the tesseract, or 8-cell, another regular four-dimensional polytope. A tesseract has cubic cells, while the 24-cell has octahedral cells. The 600-cell and 120-cell are also four-dimensional regular polytopes, but their cells are tetrahedra and dodecahedra, respectively.