As a consequence of this result, we see that the number of different labeled combinatorial types of inscribable neighborly d-polytopes with n vertices is at least [n.
1 is inspired by [GZ13, Proposition 17], where a similar argument is used to prove that the cyclic polytope is inscribable (see also [Sei85] for a related result in the plane).
Then there is an inscribable simplicial (d + 1)-polytope [P.
Observe how the strategy is to start with a k-neighborly d-polytope, lift it to a (k + 1)-neighborly (d + 1)-triangulation, and lift it again (with a positive lifting with the same order) to a (k + 1)-neighborly (d + 2)-polytope, which is inscribable.
is an inscribable (k + 1)-neighborly (d + 2)-polytope.
4, this is precisely the operation we used here construct inscribable neighborly polytopes.
4 Every Gale sewn neighborly poly tope is inscribable.