3 problems

Milman-moduli conjecture. For positive $\varepsilon$,

Day–Nordlander conjecture. The displayed inequalities hold.

Let ${\bf K}$ be an arbitrary $0$-symmetric convex body in ${\mathbb R}^3$. A truncated octahedron of the form ${\bf T}-{\bf T}$ is obtained from an arbitrary tetrahedron ${\bf T}$…