  A quandle is an algebraic system which excels at describing limited
symmetries of a space. We introduce the concept of Schl\"{a}fli 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 Schl\"{a}fli quandle
related to the regular tessellation $\{ 3, m \}$ in the sense of the
Schl\"{a}fli symbol if $m \geq 3$.
