Structure of kissing arrangements in ${\mathbb{R}}^{12}$ and a place for the $841$st sphere

Rustem Takhanov, Zhenisbek Assylbekov, Stanislav Yun

Most currently known kissing arrangements of size $840$ in ${\mathbb{R}}^{12}$ share a common structure. They consist of $60$ vectors supported on ${\mathbb{R}}^6\times \{0\}$, an…