2 problems

Minimality conjecture. The triangulated $n$-sphere constructed in Theorem is facet-minimal, and it is vertex-minimal as well.

Let $T=\triangle(,0,)$ be a triangle and denote its angle at $0$ by $\theta=\measuredangle(\xi,0,\eta)$. Let $T^q$ be the $q$th level of the regular 1-4 subdivision of $T$. For…