Bisztriczky defines a multiplex as a generalization of a simplex, and an ordinary polytope as a generalization of a cyclic polytope. This paper presents results concerning the combinatorics of multiplexes and ordinary polytopes. The flag vector of the multiplex is computed, and shown to equal the flag vector of a many-folded pyramid over a polygon. Multiplexes, but not other ordinary polytopes, are shown to be elementary. It is shown that all complete subgraphs of the graph of a multiplex determine faces of the multiplex. The toric h -vectors of the ordinary five-dimensional polytopes are given. Graphs of ordinary polytopes are studied. Their chromatic numbers and diameters are computed, and they are shown to be Hamiltonian.
Received December 8, 2000, and in revised form June 21, 2001. Online publication November 2, 2001.
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Bayer, M., Bruening, A. & Stewart, J. A Combinatorial Study of Multiplexes and Ordinary Polytopes. Discrete Comput Geom 27, 49–63 (2002). https://doi.org/10.1007/s00454-001-0051-x