The 16-cell β_4 is the finite regular four-dimensional cross polytope with Schläfli symbol {3, 3, 4}. It is also known as the hyperoctahedron or hexadecachoron, and its composed of 16 tetrahedra, with 4 to an edge. It has 8 vertices, 24 edges, and 32 faces. It is one of the six regular polychora. The 16-cell is a four-dimensional dipyramid based on the three-dimensional square dipyramid with its two apices in opposite directions along the fourth dimension. The 16-cell is the dual of the tesseract.
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