5 problems

Positivity conjecture. The only frieze patterns of Type $\Lambda_{p_1,\ldots,p_s}$ with negative entries are those which fail the realizability test. In particular, all quotient di…

Let ${\mathcal{D}}$ be a generalized dissection, let ${\mathcal{T}}({\mathcal{D}})$ be its associated constrained triangulation, and let $V({\mathcal{D}})$ and $Y({\mathcal{D}})$ d…

Non-right-dihedral gentile tetrahedra conjecture. There are no gentile tetrahedra that do not have a dihedral angle of exactly $pi/2$.

Gentile acute tetrahedra conjecture. There are no gentile acute tetrahedra.

Ten-triangle conjecture. Any dissection of an acute spherical diangle into acute spherical triangles requires at least ten triangles.