PretzelKnot

The pretzel knot $P(p,q,r)$, for odd $p,q,r$ — three twisted bands side by side, named by its closed form since no general braid word is known for the family.

PretzelKnot(p, q, r)$P(p,q,r)$ as a knot, for odd $p,q,r$

Typed signatures

Type	Package	Applies
(integer, integer, integer) -> expression<PretzelKnot>	braid	always

Domain: Braids and knots

Examples

Basic #

A genus-1 pretzel knot

live ↗

In$\mathrm{SeifertGenus}(\mathrm{PretzelKnot}(-3, 5, 7))$Out$1$

$P(1,1,1)$ has the trefoil's Alexander polynomial

live ↗

In$\mathrm{AlexanderPolynomial}(\mathrm{PretzelKnot}(1, 1, 1))$Out$t^2-t+1$

About

Examples	2

See also: TwistKnot, TorusKnot, AlexanderPolynomial