The Pretzel Knot
goodknot.bmp

Names and notations

Rolfsen notation

77

Dowker-Thistlethwaite notation

8 14 12 2 4 6 10

Conway notation

21112

Planar Graph

goodgraph.JPG

Braid notation

б-3 б2б-3 б2 б-1 б2 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

q4-2q3+3q2-4q+4-3q-1+3q-2-q-3

Alexander polynomial

t2-5t+9-5t-1+t-2

HOMFLY polynomial

m4-l2m2-2m2l-2+2m2-2l-2+l-4+2

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