The Alternating Knot 9₇

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Acknowledgement

KnotPlot

PD Presentation: X₁₄₂₅ X_3,12,4,13 X_5,16,6,17 X_7,18,8,1 X_17,6,18,7 X_9,14,10,15 X_13,10,14,11 X_15,8,16,9 X_11,2,12,3

Gauss Code: {-1, 9, -2, 1, -3, 5, -4, 8, -6, 7, -9, 2, -7, 6, -8, 3, -5, 4}

DT (Dowker-Thistlethwaite) Code: 4 12 16 18 14 2 10 8 6

Minimum Braid Representative:

Length is 11, width is 4
Braid index is 4

A Morse Link Presentation:

3D Invariants:

Symmetry Type Unknotting Number 3-Genus Bridge/Super Bridge Index Nakanishi Index

Reversible 2 2 2 / 4--6 1

Alexander Polynomial: 3t^-2 - 7t^-1 + 9 - 7t + 3t²

Conway Polynomial: 1 + 5z² + 3z⁴

Other knots with the same Alexander/Conway Polynomial: {...}

Determinant and Signature: {29, -4}

Jones Polynomial: - q^-11 + 2q^-10 - 3q^-9 + 4q^-8 - 5q^-7 + 5q^-6 - 4q^-5 + 3q^-4 - q^-3 + q^-2

Other knots (up to mirrors) with the same Jones Polynomial: {...}

A2 (sl(3)) Invariant: - q^-34 - q^-28 + q^-26 - q^-18 + q^-16 + q^-12 + 2q^-10 + q^-6

HOMFLY-PT Polynomial: 2a⁴ + 3a⁴z² + a⁴z⁴ - a⁶ + a⁶z² + a⁶z⁴ + a⁸ + 2a⁸z² + a⁸z⁴ - a¹⁰ - a¹⁰z²

Kauffman Polynomial: 2a⁴ - 3a⁴z² + a⁴z⁴ - a⁵z - a⁵z³ + a⁵z⁵ + a⁶ - 2a⁶z² + a⁶z⁶ - a⁷z + 2a⁷z³ - a⁷z⁵ + a⁷z⁷ + a⁸ - 4a⁸z² + 7a⁸z⁴ - 3a⁸z⁶ + a⁸z⁸ - 3a⁹z + 11a⁹z³ - 9a⁹z⁵ + 3a⁹z⁷ + a¹⁰ - 2a¹⁰z² + 2a¹⁰z⁴ - 2a¹⁰z⁶ + a¹⁰z⁸ - 2a¹¹z + 5a¹¹z³ - 6a¹¹z⁵ + 2a¹¹z⁷ + 3a¹²z² - 6a¹²z⁴ + 2a¹²z⁶ + a¹³z - 3a¹³z³ + a¹³z⁵

V₂ and V₃, the type 2 and 3 Vassiliev invariants: {5, -12}

Khovanov Homology:
(The squares with yellow highlighting are those on the "critical diagonals", where j-2r=s+1 or j-2r=s+1, where s=-4 is the signature of 9₇. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.)

t^rq^j r = -9 r = -8 r = -7 r = -6 r = -5 r = -4 r = -3 r = -2 r = -1 r = 0

j = -3 1

j = -5 1 1

j = -7 2

j = -9 2 1

j = -11 3 2

j = -13 2 2

j = -15 2 3

j = -17 1 2

j = -19 1 2

j = -21 1

j = -23 1

n Coloured Jones Polynomial (in the (n+1)-dimensional representation of sl(2))
2 q^-31 - 2q^-30 + 5q^-28 - 6q^-27 - 3q^-26 + 12q^-25 - 7q^-24 - 9q^-23 + 18q^-22 - 6q^-21 - 16q^-20 + 22q^-19 - 4q^-18 - 19q^-17 + 21q^-16 - 2q^-15 - 16q^-14 + 14q^-13 - 9q^-11 + 7q^-10 - 3q^-8 + 3q^-7 - q^-5 + q^-4

3 - q^-60 + 2q^-59 - 2q^-57 - 2q^-56 + 5q^-55 + 4q^-54 - 7q^-53 - 9q^-52 + 9q^-51 + 13q^-50 - 6q^-49 - 20q^-48 + 3q^-47 + 24q^-46 + 3q^-45 - 26q^-44 - 11q^-43 + 27q^-42 + 19q^-41 - 26q^-40 - 26q^-39 + 24q^-38 + 33q^-37 - 23q^-36 - 37q^-35 + 19q^-34 + 41q^-33 - 17q^-32 - 41q^-31 + 14q^-30 + 38q^-29 - 8q^-28 - 35q^-27 + 5q^-26 + 26q^-25 - 21q^-23 + q^-22 + 9q^-21 + 4q^-20 - 9q^-19 + 3q^-18 + q^-16 - 3q^-15 + 4q^-14 - q^-13 - 2q^-11 + 3q^-10 - q^-7 + q^-6

4 q^-98 - 2q^-97 + 2q^-95 - q^-94 + 3q^-93 - 7q^-92 + 7q^-90 - q^-89 + 10q^-88 - 19q^-87 - 8q^-86 + 13q^-85 + 3q^-84 + 29q^-83 - 28q^-82 - 22q^-81 + 5q^-80 - 4q^-79 + 58q^-78 - 19q^-77 - 24q^-76 - 12q^-75 - 34q^-74 + 73q^-73 + 2q^-72 + 3q^-71 - 18q^-70 - 81q^-69 + 62q^-68 + 16q^-67 + 47q^-66 - 4q^-65 - 124q^-64 + 35q^-63 + 16q^-62 + 90q^-61 + 19q^-60 - 154q^-59 + 10q^-58 + 10q^-57 + 119q^-56 + 39q^-55 - 168q^-54 - 10q^-53 + 3q^-52 + 133q^-51 + 53q^-50 - 163q^-49 - 25q^-48 - 9q^-47 + 126q^-46 + 67q^-45 - 132q^-44 - 34q^-43 - 31q^-42 + 97q^-41 + 73q^-40 - 80q^-39 - 24q^-38 - 49q^-37 + 49q^-36 + 60q^-35 - 30q^-34 - 2q^-33 - 46q^-32 + 10q^-31 + 33q^-30 - 7q^-29 + 15q^-28 - 27q^-27 - 5q^-26 + 11q^-25 - 3q^-24 + 16q^-23 - 11q^-22 - 4q^-21 + 2q^-20 - 4q^-19 + 10q^-18 - 3q^-17 - q^-16 - 3q^-14 + 4q^-13 - q^-9 + q^-8

5 - q^-145 + 2q^-144 - 2q^-142 + q^-141 - q^-139 + 3q^-138 + q^-137 - 6q^-136 - 2q^-135 + 3q^-134 + 2q^-133 + 8q^-132 + 4q^-131 - 10q^-130 - 16q^-129 - 5q^-128 + 8q^-127 + 20q^-126 + 22q^-125 - 5q^-124 - 27q^-123 - 30q^-122 - 10q^-121 + 23q^-120 + 40q^-119 + 24q^-118 - 7q^-117 - 35q^-116 - 43q^-115 - 14q^-114 + 21q^-113 + 39q^-112 + 43q^-111 + 15q^-110 - 29q^-109 - 62q^-108 - 57q^-107 - 6q^-106 + 66q^-105 + 106q^-104 + 58q^-103 - 55q^-102 - 148q^-101 - 119q^-100 + 26q^-99 + 176q^-98 + 187q^-97 + 18q^-96 - 196q^-95 - 251q^-94 - 66q^-93 + 203q^-92 + 303q^-91 + 119q^-90 - 201q^-89 - 352q^-88 - 163q^-87 + 199q^-86 + 383q^-85 + 201q^-84 - 187q^-83 - 414q^-82 - 232q^-81 + 186q^-80 + 428q^-79 + 254q^-78 - 174q^-77 - 442q^-76 - 272q^-75 + 162q^-74 + 446q^-73 + 288q^-72 - 147q^-71 - 434q^-70 - 303q^-69 + 114q^-68 + 420q^-67 + 314q^-66 - 80q^-65 - 379q^-64 - 317q^-63 + 27q^-62 + 333q^-61 + 305q^-60 + 17q^-59 - 254q^-58 - 286q^-57 - 65q^-56 + 190q^-55 + 238q^-54 + 85q^-53 - 97q^-52 - 194q^-51 - 112q^-50 + 62q^-49 + 129q^-48 + 88q^-47 + 8q^-46 - 88q^-45 - 90q^-44 - 7q^-43 + 45q^-42 + 48q^-41 + 39q^-40 - 24q^-39 - 46q^-38 - 17q^-37 + 5q^-36 + 16q^-35 + 31q^-34 - 3q^-33 - 19q^-32 - 8q^-31 - 4q^-30 + 19q^-28 + q^-27 - 7q^-26 - 2q^-25 - 3q^-24 - 4q^-23 + 9q^-22 + 2q^-21 - 2q^-20 - q^-18 - 3q^-17 + 3q^-16 + q^-15 - q^-11 + q^-10

Computer Talk. The data above can be recomputed by Mathematica using the package KnotTheory`. Following setup, the sample Mathematica session below reproduces most of the above data (Mathematica system prompts in blue, human input in red, Mathematica output in black):

In[1]:=

<< KnotTheory`

Loading KnotTheory` (version of August 30, 2005, 10:15:35)...

In[2]:=
PD[Knot[9, 7]]

Out[2]=
PD[X[1, 4, 2, 5], X[3, 12, 4, 13], X[5, 16, 6, 17], X[7, 18, 8, 1], > X[17, 6, 18, 7], X[9, 14, 10, 15], X[13, 10, 14, 11], X[15, 8, 16, 9], > X[11, 2, 12, 3]]

In[3]:=
GaussCode[Knot[9, 7]]

Out[3]=
GaussCode[-1, 9, -2, 1, -3, 5, -4, 8, -6, 7, -9, 2, -7, 6, -8, 3, -5, 4]

In[4]:=
DTCode[Knot[9, 7]]

Out[4]=
DTCode[4, 12, 16, 18, 14, 2, 10, 8, 6]

In[5]:=
br = BR[Knot[9, 7]]

Out[5]=
BR[4, {-1, -1, -1, -1, -2, 1, -2, -3, 2, -3, -3}]

In[6]:=
{First[br], Crossings[br]}

Out[6]=
{4, 11}

In[7]:=
BraidIndex[Knot[9, 7]]

Out[7]=
4

In[8]:=
Show[DrawMorseLink[Knot[9, 7]]]

Out[8]=
-Graphics-

In[9]:=
#[Knot[9, 7]]& /@ {SymmetryType, UnknottingNumber, ThreeGenus, BridgeIndex, SuperBridgeIndex, NakanishiIndex}

Out[9]=
{Reversible, 2, 2, 2, {4, 6}, 1}

In[10]:=
alex = Alexander[Knot[9, 7]][t]

Out[10]=
3 7 2 9 + -- - - - 7 t + 3 t 2 t t

In[11]:=
Conway[Knot[9, 7]][z]

Out[11]=
2 4 1 + 5 z + 3 z

In[12]:=
Select[AllKnots[], (alex === Alexander[#][t])&]

Out[12]=
{Knot[9, 7]}

In[13]:=
{KnotDet[Knot[9, 7]], KnotSignature[Knot[9, 7]]}

Out[13]=
{29, -4}

In[14]:=
Jones[Knot[9, 7]][q]

Out[14]=
-11 2 3 4 5 5 4 3 -3 -2 -q + --- - -- + -- - -- + -- - -- + -- - q + q 10 9 8 7 6 5 4 q q q q q q q

In[15]:=
Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&]

Out[15]=
{Knot[9, 7]}

In[16]:=
A2Invariant[Knot[9, 7]][q]

Out[16]=
-34 -28 -26 -18 -16 -12 2 -6 -q - q + q - q + q + q + --- + q 10 q

In[17]:=
HOMFLYPT[Knot[9, 7]][a, z]

Out[17]=
4 6 8 10 4 2 6 2 8 2 10 2 4 4 6 4 2 a - a + a - a + 3 a z + a z + 2 a z - a z + a z + a z + 8 4 > a z

In[18]:=
Kauffman[Knot[9, 7]][a, z]

Out[18]=
4 6 8 10 5 7 9 11 13 4 2 2 a + a + a + a - a z - a z - 3 a z - 2 a z + a z - 3 a z - 6 2 8 2 10 2 12 2 5 3 7 3 9 3 > 2 a z - 4 a z - 2 a z + 3 a z - a z + 2 a z + 11 a z + 11 3 13 3 4 4 8 4 10 4 12 4 5 5 > 5 a z - 3 a z + a z + 7 a z + 2 a z - 6 a z + a z - 7 5 9 5 11 5 13 5 6 6 8 6 10 6 > a z - 9 a z - 6 a z + a z + a z - 3 a z - 2 a z + 12 6 7 7 9 7 11 7 8 8 10 8 > 2 a z + a z + 3 a z + 2 a z + a z + a z

In[19]:=
{Vassiliev[2][Knot[9, 7]], Vassiliev[3][Knot[9, 7]]}

Out[19]=
{5, -12}

In[20]:=
Kh[Knot[9, 7]][q, t]

Out[20]=
-5 -3 1 1 1 2 1 2 2 q + q + ------ + ------ + ------ + ------ + ------ + ------ + ------ + 23 9 21 8 19 8 19 7 17 7 17 6 15 6 q t q t q t q t q t q t q t 3 2 2 3 2 2 1 2 1 > ------ + ------ + ------ + ------ + ------ + ----- + ----- + ----- + ---- 15 5 13 5 13 4 11 4 11 3 9 3 9 2 7 2 5 q t q t q t q t q t q t q t q t q t

In[21]:=
ColouredJones[Knot[9, 7], 2][q]

Out[21]=
-31 2 5 6 3 12 7 9 18 6 16 22 4 q - --- + --- - --- - --- + --- - --- - --- + --- - --- - --- + --- - --- - 30 28 27 26 25 24 23 22 21 20 19 18 q q q q q q q q q q q q 19 21 2 16 14 9 7 3 3 -5 -4 > --- + --- - --- - --- + --- - --- + --- - -- + -- - q + q 17 16 15 14 13 11 10 8 7 q q q q q q q q q

Dror Bar-Natan: The Knot Atlas: The Rolfsen Knot Table: The Knot 9₇

9₆
9₈

n	Coloured Jones Polynomial (in the (n+1)-dimensional representation of sl(2))
2	q^-31 - 2q^-30 + 5q^-28 - 6q^-27 - 3q^-26 + 12q^-25 - 7q^-24 - 9q^-23 + 18q^-22 - 6q^-21 - 16q^-20 + 22q^-19 - 4q^-18 - 19q^-17 + 21q^-16 - 2q^-15 - 16q^-14 + 14q^-13 - 9q^-11 + 7q^-10 - 3q^-8 + 3q^-7 - q^-5 + q^-4
3	- q^-60 + 2q^-59 - 2q^-57 - 2q^-56 + 5q^-55 + 4q^-54 - 7q^-53 - 9q^-52 + 9q^-51 + 13q^-50 - 6q^-49 - 20q^-48 + 3q^-47 + 24q^-46 + 3q^-45 - 26q^-44 - 11q^-43 + 27q^-42 + 19q^-41 - 26q^-40 - 26q^-39 + 24q^-38 + 33q^-37 - 23q^-36 - 37q^-35 + 19q^-34 + 41q^-33 - 17q^-32 - 41q^-31 + 14q^-30 + 38q^-29 - 8q^-28 - 35q^-27 + 5q^-26 + 26q^-25 - 21q^-23 + q^-22 + 9q^-21 + 4q^-20 - 9q^-19 + 3q^-18 + q^-16 - 3q^-15 + 4q^-14 - q^-13 - 2q^-11 + 3q^-10 - q^-7 + q^-6
4	q^-98 - 2q^-97 + 2q^-95 - q^-94 + 3q^-93 - 7q^-92 + 7q^-90 - q^-89 + 10q^-88 - 19q^-87 - 8q^-86 + 13q^-85 + 3q^-84 + 29q^-83 - 28q^-82 - 22q^-81 + 5q^-80 - 4q^-79 + 58q^-78 - 19q^-77 - 24q^-76 - 12q^-75 - 34q^-74 + 73q^-73 + 2q^-72 + 3q^-71 - 18q^-70 - 81q^-69 + 62q^-68 + 16q^-67 + 47q^-66 - 4q^-65 - 124q^-64 + 35q^-63 + 16q^-62 + 90q^-61 + 19q^-60 - 154q^-59 + 10q^-58 + 10q^-57 + 119q^-56 + 39q^-55 - 168q^-54 - 10q^-53 + 3q^-52 + 133q^-51 + 53q^-50 - 163q^-49 - 25q^-48 - 9q^-47 + 126q^-46 + 67q^-45 - 132q^-44 - 34q^-43 - 31q^-42 + 97q^-41 + 73q^-40 - 80q^-39 - 24q^-38 - 49q^-37 + 49q^-36 + 60q^-35 - 30q^-34 - 2q^-33 - 46q^-32 + 10q^-31 + 33q^-30 - 7q^-29 + 15q^-28 - 27q^-27 - 5q^-26 + 11q^-25 - 3q^-24 + 16q^-23 - 11q^-22 - 4q^-21 + 2q^-20 - 4q^-19 + 10q^-18 - 3q^-17 - q^-16 - 3q^-14 + 4q^-13 - q^-9 + q^-8
5	- q^-145 + 2q^-144 - 2q^-142 + q^-141 - q^-139 + 3q^-138 + q^-137 - 6q^-136 - 2q^-135 + 3q^-134 + 2q^-133 + 8q^-132 + 4q^-131 - 10q^-130 - 16q^-129 - 5q^-128 + 8q^-127 + 20q^-126 + 22q^-125 - 5q^-124 - 27q^-123 - 30q^-122 - 10q^-121 + 23q^-120 + 40q^-119 + 24q^-118 - 7q^-117 - 35q^-116 - 43q^-115 - 14q^-114 + 21q^-113 + 39q^-112 + 43q^-111 + 15q^-110 - 29q^-109 - 62q^-108 - 57q^-107 - 6q^-106 + 66q^-105 + 106q^-104 + 58q^-103 - 55q^-102 - 148q^-101 - 119q^-100 + 26q^-99 + 176q^-98 + 187q^-97 + 18q^-96 - 196q^-95 - 251q^-94 - 66q^-93 + 203q^-92 + 303q^-91 + 119q^-90 - 201q^-89 - 352q^-88 - 163q^-87 + 199q^-86 + 383q^-85 + 201q^-84 - 187q^-83 - 414q^-82 - 232q^-81 + 186q^-80 + 428q^-79 + 254q^-78 - 174q^-77 - 442q^-76 - 272q^-75 + 162q^-74 + 446q^-73 + 288q^-72 - 147q^-71 - 434q^-70 - 303q^-69 + 114q^-68 + 420q^-67 + 314q^-66 - 80q^-65 - 379q^-64 - 317q^-63 + 27q^-62 + 333q^-61 + 305q^-60 + 17q^-59 - 254q^-58 - 286q^-57 - 65q^-56 + 190q^-55 + 238q^-54 + 85q^-53 - 97q^-52 - 194q^-51 - 112q^-50 + 62q^-49 + 129q^-48 + 88q^-47 + 8q^-46 - 88q^-45 - 90q^-44 - 7q^-43 + 45q^-42 + 48q^-41 + 39q^-40 - 24q^-39 - 46q^-38 - 17q^-37 + 5q^-36 + 16q^-35 + 31q^-34 - 3q^-33 - 19q^-32 - 8q^-31 - 4q^-30 + 19q^-28 + q^-27 - 7q^-26 - 2q^-25 - 3q^-24 - 4q^-23 + 9q^-22 + 2q^-21 - 2q^-20 - q^-18 - 3q^-17 + 3q^-16 + q^-15 - q^-11 + q^-10

In[1]:=	<< KnotTheory`
Loading KnotTheory` (version of August 30, 2005, 10:15:35)...
In[2]:=	PD[Knot[9, 7]]
Out[2]=	PD[X[1, 4, 2, 5], X[3, 12, 4, 13], X[5, 16, 6, 17], X[7, 18, 8, 1], > X[17, 6, 18, 7], X[9, 14, 10, 15], X[13, 10, 14, 11], X[15, 8, 16, 9], > X[11, 2, 12, 3]]
In[3]:=	GaussCode[Knot[9, 7]]
Out[3]=	GaussCode[-1, 9, -2, 1, -3, 5, -4, 8, -6, 7, -9, 2, -7, 6, -8, 3, -5, 4]
In[4]:=	DTCode[Knot[9, 7]]
Out[4]=	DTCode[4, 12, 16, 18, 14, 2, 10, 8, 6]
In[5]:=	br = BR[Knot[9, 7]]
Out[5]=	BR[4, {-1, -1, -1, -1, -2, 1, -2, -3, 2, -3, -3}]
In[6]:=	{First[br], Crossings[br]}
Out[6]=	{4, 11}
In[7]:=	BraidIndex[Knot[9, 7]]
Out[7]=	4
In[8]:=	Show[DrawMorseLink[Knot[9, 7]]]

Out[8]=	-Graphics-
In[9]:=	#[Knot[9, 7]]& /@ {SymmetryType, UnknottingNumber, ThreeGenus, BridgeIndex, SuperBridgeIndex, NakanishiIndex}
Out[9]=	{Reversible, 2, 2, 2, {4, 6}, 1}
In[10]:=	alex = Alexander[Knot[9, 7]][t]
Out[10]=	3 7 2 9 + -- - - - 7 t + 3 t 2 t t
In[11]:=	Conway[Knot[9, 7]][z]
Out[11]=	2 4 1 + 5 z + 3 z
In[12]:=	Select[AllKnots[], (alex === Alexander[#][t])&]
Out[12]=	{Knot[9, 7]}
In[13]:=	{KnotDet[Knot[9, 7]], KnotSignature[Knot[9, 7]]}
Out[13]=	{29, -4}
In[14]:=	Jones[Knot[9, 7]][q]
Out[14]=	-11 2 3 4 5 5 4 3 -3 -2 -q + --- - -- + -- - -- + -- - -- + -- - q + q 10 9 8 7 6 5 4 q q q q q q q
In[15]:=	Select[AllKnots[], (J === Jones[#][q] \|\| (J /. q-> 1/q) === Jones[#][q])&]
Out[15]=	{Knot[9, 7]}
In[16]:=	A2Invariant[Knot[9, 7]][q]
Out[16]=	-34 -28 -26 -18 -16 -12 2 -6 -q - q + q - q + q + q + --- + q 10 q
In[17]:=	HOMFLYPT[Knot[9, 7]][a, z]
Out[17]=	4 6 8 10 4 2 6 2 8 2 10 2 4 4 6 4 2 a - a + a - a + 3 a z + a z + 2 a z - a z + a z + a z + 8 4 > a z
In[18]:=	Kauffman[Knot[9, 7]][a, z]
Out[18]=	4 6 8 10 5 7 9 11 13 4 2 2 a + a + a + a - a z - a z - 3 a z - 2 a z + a z - 3 a z - 6 2 8 2 10 2 12 2 5 3 7 3 9 3 > 2 a z - 4 a z - 2 a z + 3 a z - a z + 2 a z + 11 a z + 11 3 13 3 4 4 8 4 10 4 12 4 5 5 > 5 a z - 3 a z + a z + 7 a z + 2 a z - 6 a z + a z - 7 5 9 5 11 5 13 5 6 6 8 6 10 6 > a z - 9 a z - 6 a z + a z + a z - 3 a z - 2 a z + 12 6 7 7 9 7 11 7 8 8 10 8 > 2 a z + a z + 3 a z + 2 a z + a z + a z
In[19]:=	{Vassiliev[2][Knot[9, 7]], Vassiliev[3][Knot[9, 7]]}
Out[19]=	{5, -12}
In[20]:=	Kh[Knot[9, 7]][q, t]
Out[20]=	-5 -3 1 1 1 2 1 2 2 q + q + ------ + ------ + ------ + ------ + ------ + ------ + ------ + 23 9 21 8 19 8 19 7 17 7 17 6 15 6 q t q t q t q t q t q t q t 3 2 2 3 2 2 1 2 1 > ------ + ------ + ------ + ------ + ------ + ----- + ----- + ----- + ---- 15 5 13 5 13 4 11 4 11 3 9 3 9 2 7 2 5 q t q t q t q t q t q t q t q t q t
In[21]:=	ColouredJones[Knot[9, 7], 2][q]
Out[21]=	-31 2 5 6 3 12 7 9 18 6 16 22 4 q - --- + --- - --- - --- + --- - --- - --- + --- - --- - --- + --- - --- - 30 28 27 26 25 24 23 22 21 20 19 18 q q q q q q q q q q q q 19 21 2 16 14 9 7 3 3 -5 -4 > --- + --- - --- - --- + --- - --- + --- - -- + -- - q + q 17 16 15 14 13 11 10 8 7 q q q q q q q q q

The Alternating Knot 97

The Alternating Knot 9₇