# Conjugacy Class 3 of Group S4Z2

Cable 1:[4, 2, 3, 1, 6, 5].
Disjoint cycle form: [[1, 4], [5, 6]].
Cable 2:[2, 3, 4, 1, 5, 6].
Disjoint cycle form: [[1, 2, 3, 4]].
• Example 3_1
CC2_CLASS = 3, example 1:
Strut: [2, 1, 4, 3, 5, 6]. 	 Disjoint cycle form:  [[1, 2], [3, 4]].
Cable 1: [4, 2, 3, 1, 6, 5]. 	 Disjoint cycle form:  [[1, 4], [5, 6]].
Cable 2: [2, 3, 4, 1, 5, 6]. 	 Disjoint cycle form:  [[1, 2, 3, 4]].
Smallest equilibrium strut stress w1_min is .333333 occurring in representation dim3a.
POSSIBLE TIE involving representations: [dim3a, dim3ar]

VERTEX OVERLAP: 1 other vertice(s) coincide with basepoint.

• Example 3_2
CC2_CLASS = 3, example 2:
Strut: [3, 4, 1, 2, 6, 5]. 	 Disjoint cycle form:  [[1, 3], [2, 4], [5, 6]].
Cable 1: [4, 2, 3, 1, 6, 5]. 	 Disjoint cycle form:  [[1, 4], [5, 6]].
Cable 2: [2, 3, 4, 1, 5, 6]. 	 Disjoint cycle form:  [[1, 2, 3, 4]].
Smallest equilibrium strut stress w1_min is .177124 occurring in representation dim2r.

VERTEX OVERLAP: 3 other vertice(s) coincide with basepoint.

• Example 3_3
CC2_CLASS = 3, example 3:
Strut: [1, 2, 4, 3, 5, 6]. 	 Disjoint cycle form:  [[3, 4]].
Cable 1: [4, 2, 3, 1, 6, 5]. 	 Disjoint cycle form:  [[1, 4], [5, 6]].
Cable 2: [2, 3, 4, 1, 5, 6]. 	 Disjoint cycle form:  [[1, 2, 3, 4]].
Smallest equilibrium strut stress w1_min is .285714 occurring in representation dim2r.

VERTEX OVERLAP: 3 other vertice(s) coincide with basepoint.

• Example 3_4
CC2_CLASS = 3, example 4:
Strut: [2, 1, 3, 4, 6, 5]. 	 Disjoint cycle form:  [[1, 2], [5, 6]].
Cable 1: [4, 2, 3, 1, 6, 5]. 	 Disjoint cycle form:  [[1, 4], [5, 6]].
Cable 2: [2, 3, 4, 1, 5, 6]. 	 Disjoint cycle form:  [[1, 2, 3, 4]].
Smallest equilibrium strut stress w1_min is .4 occurring in representation dim2r.

VERTEX OVERLAP: 3 other vertice(s) coincide with basepoint.

• Example 3_5
CC2_CLASS = 3, example 5:
Strut: [4, 2, 1, 3, 5, 6]. 	 Disjoint cycle form:  [[1, 4, 3]].
Cable 1: [4, 2, 3, 1, 6, 5]. 	 Disjoint cycle form:  [[1, 4], [5, 6]].
Cable 2: [2, 3, 4, 1, 5, 6]. 	 Disjoint cycle form:  [[1, 2, 3, 4]].
Smallest equilibrium strut stress w1_min is .118082 occurring in representation dim2r.

VERTEX OVERLAP: 3 other vertice(s) coincide with basepoint.

• Example 3_6
CC2_CLASS = 3, example 6:
Strut: [1, 4, 3, 2, 6, 5]. 	 Disjoint cycle form:  [[2, 4], [5, 6]].
Cable 1: [4, 2, 3, 1, 6, 5]. 	 Disjoint cycle form:  [[1, 4], [5, 6]].
Cable 2: [2, 3, 4, 1, 5, 6]. 	 Disjoint cycle form:  [[1, 2, 3, 4]].
Smallest equilibrium strut stress w1_min is .181818 occurring in representation dim2r.

VERTEX OVERLAP: 3 other vertice(s) coincide with basepoint.

• Example 3_7
CC2_CLASS = 3, example 7:
Strut: [3, 4, 1, 2, 5, 6]. 	 Disjoint cycle form:  [[1, 3], [2, 4]].
Cable 1: [4, 2, 3, 1, 6, 5]. 	 Disjoint cycle form:  [[1, 4], [5, 6]].
Cable 2: [2, 3, 4, 1, 5, 6]. 	 Disjoint cycle form:  [[1, 2, 3, 4]].
Smallest equilibrium strut stress w1_min is 1 occurring in representation dim3a.
POSSIBLE TIE involving representations: [dim3a, dim3b, dim3ar]

VERTEX OVERLAP: 3 other vertice(s) coincide with basepoint.
DEGENERATE EDGES: 1 edge(s) of length 0.

• Example 3_8
CC2_CLASS = 3, example 8:
Strut: [1, 4, 2, 3, 5, 6]. 	 Disjoint cycle form:  [[2, 4, 3]].
Cable 1: [4, 2, 3, 1, 6, 5]. 	 Disjoint cycle form:  [[1, 4], [5, 6]].
Cable 2: [2, 3, 4, 1, 5, 6]. 	 Disjoint cycle form:  [[1, 2, 3, 4]].
Smallest equilibrium strut stress w1_min is .118082 occurring in representation dim2r.

VERTEX OVERLAP: 3 other vertice(s) coincide with basepoint.

• Example 3_9
CC2_CLASS = 3, example 9:
Strut: [3, 1, 4, 2, 6, 5]. 	 Disjoint cycle form:  [[1, 3, 4, 2], [5, 6]].
Cable 1: [4, 2, 3, 1, 6, 5]. 	 Disjoint cycle form:  [[1, 4], [5, 6]].
Cable 2: [2, 3, 4, 1, 5, 6]. 	 Disjoint cycle form:  [[1, 2, 3, 4]].
Smallest equilibrium strut stress w1_min is .292893 occurring in representation dim3a.
POSSIBLE TIE involving representations: [dim3a, dim3ar]

VERTEX OVERLAP: 1 other vertice(s) coincide with basepoint.

• Example 3_10
CC2_CLASS = 3, example 10:
Strut: [1, 3, 2, 4, 5, 6]. 	 Disjoint cycle form:  [[2, 3]].
Cable 1: [4, 2, 3, 1, 6, 5]. 	 Disjoint cycle form:  [[1, 4], [5, 6]].
Cable 2: [2, 3, 4, 1, 5, 6]. 	 Disjoint cycle form:  [[1, 2, 3, 4]].
Smallest equilibrium strut stress w1_min is .2 occurring in representation dim2r.

VERTEX OVERLAP: 3 other vertice(s) coincide with basepoint.

• Example 3_11
CC2_CLASS = 3, example 11:
Strut: [3, 1, 2, 4, 6, 5]. 	 Disjoint cycle form:  [[1, 3, 2], [5, 6]].
Cable 1: [4, 2, 3, 1, 6, 5]. 	 Disjoint cycle form:  [[1, 4], [5, 6]].
Cable 2: [2, 3, 4, 1, 5, 6]. 	 Disjoint cycle form:  [[1, 2, 3, 4]].
Smallest equilibrium strut stress w1_min is .354248 occurring in representation dim2r.

VERTEX OVERLAP: 3 other vertice(s) coincide with basepoint.

• Example 3_12
CC2_CLASS = 3, example 12:
Strut: [4, 1, 2, 3, 6, 5]. 	 Disjoint cycle form:  [[1, 4, 3, 2], [5, 6]].
Cable 1: [4, 2, 3, 1, 6, 5]. 	 Disjoint cycle form:  [[1, 4], [5, 6]].
Cable 2: [2, 3, 4, 1, 5, 6]. 	 Disjoint cycle form:  [[1, 2, 3, 4]].
Smallest equilibrium strut stress w1_min is .090909 occurring in representation dim2r.

VERTEX OVERLAP: 3 other vertice(s) coincide with basepoint.

• Example 3_13
CC2_CLASS = 3, example 13:
Strut: [3, 2, 4, 1, 6, 5]. 	 Disjoint cycle form:  [[1, 3, 4], [5, 6]].
Cable 1: [4, 2, 3, 1, 6, 5]. 	 Disjoint cycle form:  [[1, 4], [5, 6]].
Cable 2: [2, 3, 4, 1, 5, 6]. 	 Disjoint cycle form:  [[1, 2, 3, 4]].
Smallest equilibrium strut stress w1_min is .198062 occurring in representation dim3ar.

• Example 3_14
CC2_CLASS = 3, example 14:
Strut: [4, 3, 2, 1, 5, 6]. 	 Disjoint cycle form:  [[1, 4], [2, 3]].
Cable 1: [4, 2, 3, 1, 6, 5]. 	 Disjoint cycle form:  [[1, 4], [5, 6]].
Cable 2: [2, 3, 4, 1, 5, 6]. 	 Disjoint cycle form:  [[1, 2, 3, 4]].
Smallest equilibrium strut stress w1_min is .292893 occurring in representation dim3a.
POSSIBLE TIE involving representations: [dim3a, dim3ar]

VERTEX OVERLAP: 1 other vertice(s) coincide with basepoint.

• Example 3_15
CC2_CLASS = 3, example 15:
Strut: [2, 4, 1, 3, 5, 6]. 	 Disjoint cycle form:  [[1, 2, 4, 3]].
Cable 1: [4, 2, 3, 1, 6, 5]. 	 Disjoint cycle form:  [[1, 4], [5, 6]].
Cable 2: [2, 3, 4, 1, 5, 6]. 	 Disjoint cycle form:  [[1, 2, 3, 4]].
Smallest equilibrium strut stress w1_min is .1 occurring in representation dim2r.

VERTEX OVERLAP: 3 other vertice(s) coincide with basepoint.

• Example 3_16
CC2_CLASS = 3, example 16:
Strut: [3, 2, 1, 4, 5, 6]. 	 Disjoint cycle form:  [[1, 3]].
Cable 1: [4, 2, 3, 1, 6, 5]. 	 Disjoint cycle form:  [[1, 4], [5, 6]].
Cable 2: [2, 3, 4, 1, 5, 6]. 	 Disjoint cycle form:  [[1, 2, 3, 4]].
Smallest equilibrium strut stress w1_min is .310102 occurring in representation dim3ar.

• Example 3_17
CC2_CLASS = 3, example 17:
Strut: [1, 3, 2, 4, 6, 5]. 	 Disjoint cycle form:  [[2, 3], [5, 6]].
Cable 1: [4, 2, 3, 1, 6, 5]. 	 Disjoint cycle form:  [[1, 4], [5, 6]].
Cable 2: [2, 3, 4, 1, 5, 6]. 	 Disjoint cycle form:  [[1, 2, 3, 4]].
Smallest equilibrium strut stress w1_min is .333333 occurring in representation dim3a.
POSSIBLE TIE involving representations: [dim3a, dim3ar]

VERTEX OVERLAP: 1 other vertice(s) coincide with basepoint.

• Example 3_18
CC2_CLASS = 3, example 18:
Strut: [4, 2, 3, 1, 5, 6]. 	 Disjoint cycle form:  [[1, 4]].
Cable 1: [4, 2, 3, 1, 6, 5]. 	 Disjoint cycle form:  [[1, 4], [5, 6]].
Cable 2: [2, 3, 4, 1, 5, 6]. 	 Disjoint cycle form:  [[1, 2, 3, 4]].
Smallest equilibrium strut stress w1_min is .2 occurring in representation dim2r.

VERTEX OVERLAP: 3 other vertice(s) coincide with basepoint.

• Example 3_19
CC2_CLASS = 3, example 19:
Strut: [4, 3, 1, 2, 5, 6]. 	 Disjoint cycle form:  [[1, 4, 2, 3]].
Cable 1: [4, 2, 3, 1, 6, 5]. 	 Disjoint cycle form:  [[1, 4], [5, 6]].
Cable 2: [2, 3, 4, 1, 5, 6]. 	 Disjoint cycle form:  [[1, 2, 3, 4]].
Smallest equilibrium strut stress w1_min is .142857 occurring in representation dim2r.

VERTEX OVERLAP: 3 other vertice(s) coincide with basepoint.

• Example 3_20
CC2_CLASS = 3, example 20:
Strut: [4, 3, 2, 1, 6, 5]. 	 Disjoint cycle form:  [[1, 4], [2, 3], [5, 6]].
Cable 1: [4, 2, 3, 1, 6, 5]. 	 Disjoint cycle form:  [[1, 4], [5, 6]].
Cable 2: [2, 3, 4, 1, 5, 6]. 	 Disjoint cycle form:  [[1, 2, 3, 4]].
Smallest equilibrium strut stress w1_min is .177124 occurring in representation dim2r.

VERTEX OVERLAP: 3 other vertice(s) coincide with basepoint.

• Example 3_21
CC2_CLASS = 3, example 21:
Strut: [1, 2, 3, 4, 6, 5]. 	 Disjoint cycle form:  [[5, 6]].
Cable 1: [4, 2, 3, 1, 6, 5]. 	 Disjoint cycle form:  [[1, 4], [5, 6]].
Cable 2: [2, 3, 4, 1, 5, 6]. 	 Disjoint cycle form:  [[1, 2, 3, 4]].
Smallest equilibrium strut stress w1_min is .177124 occurring in representation dim2r.

VERTEX OVERLAP: 3 other vertice(s) coincide with basepoint.

• Example 3_22
CC2_CLASS = 3, example 22:
Strut: [4, 3, 1, 2, 6, 5]. 	 Disjoint cycle form:  [[1, 4, 2, 3], [5, 6]].
Cable 1: [4, 2, 3, 1, 6, 5]. 	 Disjoint cycle form:  [[1, 4], [5, 6]].
Cable 2: [2, 3, 4, 1, 5, 6]. 	 Disjoint cycle form:  [[1, 2, 3, 4]].
Smallest equilibrium strut stress w1_min is .2 occurring in representation dim2r.

VERTEX OVERLAP: 3 other vertice(s) coincide with basepoint.

• Example 3_23
CC2_CLASS = 3, example 23:
Strut: [2, 1, 4, 3, 6, 5]. 	 Disjoint cycle form:  [[1, 2], [3, 4], [5, 6]].
Cable 1: [4, 2, 3, 1, 6, 5]. 	 Disjoint cycle form:  [[1, 4], [5, 6]].
Cable 2: [2, 3, 4, 1, 5, 6]. 	 Disjoint cycle form:  [[1, 2, 3, 4]].
Smallest equilibrium strut stress w1_min is .177124 occurring in representation dim2r.

VERTEX OVERLAP: 3 other vertice(s) coincide with basepoint.