McMullen's conditions and some lower bounds for general convex polytopes
We give a lower bound for the number of vertices of a general d-dimensional polytope with a given number m of i-faces for each i=0,....,[d/2]-1. The tightness of those bounds is proved using McMullen's conditions. For m greater than a small constant, those lower bounds are attained by simplicial i-neighbourly polytopes.
Record created on 2006-02-13, modified on 2016-08-08