The knot quandle of the twist-spun trefoil is a central extension of a Schläfli quandle

Abstract

A quandle is an algebraic system which excels at describing limited symmetries of a space. We introduce the concept of Schläfli quandles which are defined relating to chosen rotational symmetries of regular tessellations. On the other hand, quandles have a good chemistry with knot theory. Associated with a knot we have its knot quandle. We show that the knot quandle of the $m$-twist-spun trefoil is a central extension of the Schläfli quandle related to the regular tessellation $\{3,m\}$ in the sense of the Schläfli symbol if $m\ge 3$.

This paper stands as a completely revised version of arXiv:1808.06276 (12 pages, 4 figures)