A cyclic polytope 
is the convex hull of 
distinct points on the moment curve in 
. The name also denotes the resulting combinatorial type.
A realization of that type as an inscribed polytope
need not itself have its vertices on the moment
curve (Medgyes 2026).
Medgyes (2026) proved that every inscribed polytope of cyclic type 
with vertices on the unit hypersphere 
has content
at most 
.
This is smaller than the unrestricted seven-vertex maximum 
. Consequently no seven-vertex inscribed
polytope maximizing that content is cyclic. Medgyes
(2026) reports AI assistance with mathematical discussions and implementation of
the certificate computations.
