The Pretzel Knot

Table of Contents

# Names and notations

## Rolfsen notation

7_{7}

## Dowker-Thistlethwaite notation

8 14 12 2 4 6 10

## Conway notation

21112

## Planar Graph

## Braid notation

б^{-3} б^{2}б^{-3} б^{2} б^{-1} б^{2} б^{-1}

# Knot properties

## Alternating knot

Yes

## Tricolorable

Yes

## Amphicheiral

No

# Numerical knot invariants

## Unknotting number

1

## Bridge number

2

## Crossing number

7

## Genus

2

# Knot polynomials

## Jones polynomial

q^{4}-2q^{3}+3q^{2}-4q+4-3q^{-1}+3q^{-2}-q^{-3}

## Alexander polynomial

t^{2}-5t+9-5t^{-1}+t^{-2}

## HOMFLY polynomial

m^{4}-l^{2}m^{2}-2m^{2}l^{-2}+2m^{2}-2l^{-2}+l^{-4}+2

page revision: 81, last edited: 04 May 2009 22:26