4 problems

Finiteness conjecture. In this case, ${\mit \Gamma}$ is finite if and only if $(s,t)=(1,2),(1,3),(1,4)$ or $(2,3)$, up to interchanging $s$ and $t$. This is a concrete instance of…

Let $\alpha$, $\beta$, and $\gamma$ be the three generators constructed from the elements in the preceding construction, and let $\langle\alpha,\beta,\gamma\rangle$ denote the subg…

Primitive-element square conjecture. There exist such $j_1$ and $j_2$ for which

Let $G\cong PSL(2,q)$ with $q=p^d$ and $d>1$. A chiral polytope existence conjecture asserts that $G$ is the automorphism group of a chiral polytope of rank $4$ if and only if one…