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Apr 2, 2021 at 18:40 comment added Sam Hopkins What Fedor says is of course true, but might be worth adding that the cyclic polytopes simultaneously maximize the face numbers of all dimensions at once.
Apr 2, 2021 at 12:52 comment added Fedor Petrov Maximum number of facets is achieved for a cyclic polytope, this is a famous result by P. McMullen cambridge.org/core/journals/mathematika/article/…
Apr 2, 2021 at 12:08 comment added Turbo @FedorPetrov What is the general situation for minimality?
Apr 2, 2021 at 12:03 comment added Fedor Petrov Say, if $k=2$, the answer is $d$, not $d(d-1)/2$
Apr 2, 2021 at 11:18 comment added Turbo Is there a notion of minimality?
Apr 2, 2021 at 11:17 history answered Alexandre Eremenko CC BY-SA 4.0