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A finite regular 4-D Polytope with Schläfli Symbol 
. Coxeter (1969) gives
a list of the Vertex positions. The Even coefficients of the 
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
References
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.''
http://www.research.att.com/~njas/sequences/eisonline.html and extended entry in
Sloane, N. J. A. and Plouffe, S.
The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.