geometry-topology / Metric geometry
Let $U_n\subset\mathbb R^n$ be the dual of the difference polytope of a regular $n$-simplex such that $U_n$ circumscribes a sphere of diameter 1. Then every set of diameter 1 in $\mathbb R^n$ is covered by a rotated copy of $U_n$.
Temporal state
No reconciled state yet.
Append-only history
Makeev conjectured it to be true for all dimensions. This result disproves it for dimensions 4 and 5. Dimensions 6 and above remain open.
Research memory
Let $U_n\subset\mathbb R^n$ be the dual of the difference polytope of a regular $n$-simplex such that $U_n$ circumscribes a sphere of diameter 1. Then every set of diameter 1 in $\mathbb R^n$ is covered by a rotated copy of $U_n$.
Makeev conjectured it to be true for all dimensions. This result disproves it for dimensions 4 and 5. Dimensions 6 and above remain open.
Evidence graph
No public relationships recorded yet.