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A finite regular 4-D Polytope with Schläfli Symbol $\{3, 4, 3\}$. Coxeter (1969) gives a list of the Vertex positions. The Even coefficients of the $D_4$ lattice are 1, 24, 24, 96, ... (Sloane's A004011), and the 24 shortest vectors in this lattice form the 24-cell (Coxeter 1973, Conway and Sloane 1993, Sloane and Plouffe 1995).

See also 16-Cell, 120-Cell, 600-Cell, Cell, Polytope


Conway, J. H. and Sloane, N. J. A. Sphere-Packings, Lattices and Groups, 2nd ed. New York: Springer-Verlag, 1993.

Coxeter, H. S. M. Introduction to Geometry, 2nd ed. New York: Wiley, p. 404, 1969.

Coxeter, H. S. M. Regular Polytopes, 3rd ed. New York: Dover, 1973.

Sloane, N. J. A. Sequence A004011/M5140 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' and extended entry in Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.

© 1996-9 Eric W. Weisstein