Quotient graphs and amalgam presentations for unitary groups over cyclotomic rings

Suppose $4\mathrm{\mid }n$, $n\ge 8$, $F=F_n=\mathbb{Q}({\zeta }_n+{\bar{\zeta }}_n)$, and there is one prime $\mathfrak{p}={\mathfrak{p}}_n$ above $2$ in $F_n$. We study amalgam presentations for $\mathrm{}(\mathbb{Z}[{\zeta }_n,1\mathrm{/}2])$ and $\mathrm{}(\mathbb{Z}[{\zeta }_n,1\mathrm{/}2])$ with the Clifford-cyclotomic group in quantum computing as a subgroup. These amalgams arise from an action of these groups on the Bruhat-Tits tree $\mathrm{\Delta }={\mathrm{\Delta }}_{\mathfrak{p}}$ for $\mathrm{}(F_{\mathfrak{p}})$ constructed via the Hamilton quaternions. We explicitly compute the finite quotient graphs and the resulting amalgams for $8\le n\le 48$, $n\mathrm{\ne }44$, as well as for $\mathrm{}(\mathbb{Z}[{\zeta }_{60},1\mathrm{/}2])$.