On the knot quandle of the twist-spun trefoil

Ayumu Inoue

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arXiv · 1808.06276

On the knot quandle of the twist-spun trefoil

Ayumu Inoue

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Abstract

We show that the knot quandle of the $3$-, $4$-, or $5$-twist-spun trefoil is isomorphic to a quandle related to the $16$-, $24$-, or $600$-cell respectively. We further show that the cardinality of the knot quandle of the $m$-twist-spun trefoil is finite if and only if $1 \leq m \leq 5$. This phenomenon is attributable to the fact that the regular tessellation $\{ 3, m \}$, in the sense of the Schl\"{a}fli symbol, consists of infinite triangles if $m$ is greater than or equal to 6.

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Ayumu Inoue. 2018-08-20. On the knot quandle of the twist-spun trefoil. https://arxiv.org/abs/1808.06276

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