3-valent: 3 axes of symmetry: *"(7,7,7)" 1 axis of symmetry: *"(7,6,6)" no axis of symmetry: *"(14,6,4") 4-valent: 4 axes of symmetry: *"(5,5,5,5)" 2 axes of symmetry; diagonal: *"(7,3,7,3)" 1 axis of symmetry; orthogonal: *"(6,6,4,4)" 1 axis of symmetry; diagonal: *"(7,4,3,4)", "(5,4,4,4)" *"(3,6,6,6) (0 1)(2)(3)" no axis of symmetry: *"(10,8,6,4)", "(8,6,4,4)" *"(8,6,4,4) (3)", "(6,4,4,4) (3)" *"(3,6,6,6) (0 1)(3)" 5-valent: 5 axes of symmetry: *"(4,4,4,4,4)" 1 axis of symmetry: *"(6,3,6,4,4)", "(3,4,4,4,4)", "(6,6,4,4,4)", "(6,4,6,4,4)" *"(3,4,4,4,4) (0 1)(2)(3)(4)" *"(6,6,3,3,3) (0 2)(1)(3)(4)" *"(5,3,5,3,3) (0 1)(2 3)(4)" no axis of symmetry; chiral: *"(5,3,4,3,3) (0 1)(2 3)(4)", "(7,3,3,3,3) (0 1)(2 3)(4)" no axis of symmetry: *"(12,10,8,6,4)", "(8,6,4,4,4)", "(8,4,6,4,4)", "(8,6,6,4,4)", "(8,6,4,6,4)", "(10,8,6,4,4)", "(10,8,4,6,4)" *"(10,8,6,4,4) (4)", "(6,4,4,4,4) (4)", "(6,6,4,4,4) (4)", "(8,6,4,4,4) (4)", "(8,4,6,4,4) (4)", "(8,6,6,4,4) (4)" *"(8,4,6,6,6) (3)(4)", "(4,6,6,6,6) (3)(4)" *"(6,8,8,4,4) (2)(4)", "(8,8,4,4,4) (1)(4)" *"(8,6,4,3,4) (3 4)", "(6,4,4,4,4) (3 4)", "(6,4,6,4,4) (0 1)", "(8,6,4,4,4) (3 4)", "(3,4,6,4,4) (0 1)", "(8,6,4,6,4) (3 4)" *"(8,4,6,6,6) [3 4]", "(4,6,6,6,6) [3 4]" *"(6,8,4,8,4) [2 4]", "(8,4,8,4,4) [0 2]" *"(3,6,4,6,6) (0 1)(4)", "(3,6,6,6,6) (0 1)(4)", "(4,6,6,6,6) (2 3)(4)", "(4,6,4,6,6) (0 1)(4)" *"(4,4,6,6,6) (0 2)(4)" *"(4,8,8,8,8) [2 3](4)" *"(4,6,4,6,6) [0 2](4)" *"(3,8,8,8,8) (0 1)(3)(4)" *"(4,4,6,6,6) (0 2)(1)(4)" *"(4,6,3,6,6) (0 1)(2 3)", "(3,6,6,6,6) (0 1)(3 4)" *"(3,8,8,8,8) (0 1)[3 4]" *"(3,4,4,4,4) (0 1)[2 3](4)" 6-valent: 6 axes of symmetry: *"(4,4,4,4,4,4)" 3 axes of symmetry; diagonal: *"(4,3,4,3,4,3)" 2 axes of symmetry: *"(3,4,4,3,4,4)" 1 axis of symmetry; orthogonal: *"(6,8,8,6,4,4)", "(6,6,4,4,4,4)" *"(6,6,4,4,4,4) (0 2)(1)(3)(4)(5)" 1 axis of symmetry; diagonal: *"(5,4,6,3,6,4)", "(3,4,4,4,4,4)", "(6,4,6,4,4,4)", "(6,6,6,4,4,4)", "(5,4,4,3,4,4)", "(6,3,6,4,4,4)", "(3,4,6,4,6,4)", ("6,3,6,4,3,4") *"(3,5,5,5,5,5) (0 1)(2)(3)(4)(5)" *"(6,6,6,3,3,3) (0 3)(1)(2)(4)(5)" *"(3,4,3,4,4,4) (0 1)(2 3)(4)(5)" *"(5,4,4,3,4,4) (0 1)(2)(3 4)(5)", "(3,4,4,4,4,4) (0 1)(2)(3 4)(5)" *"(4,5,4,3,3,3) (0 3)(1 2)(4)(5)", "(3,6,6,6,6,6) (0 1)(2 5)(3)(4)", "(4,3,4,3,3,3) (0 3)(1 2)(4)(5)", "(3,3,3,4,4,4) (0 3)(1)(2)(4 5)" *"(5,3,4,3,4,3) (0 1)(2 3)(4 5)", "(4,3,3,3,3,3) (0 1)(2 3)(4 5)", "(4,3,4,3,3,3) (0 1)(2 3)(4 5)" *"(3,5,5,5,5,5) (0 1)(2 4)(3 5)" no axis of symmetry; 2-fold rotational symmetry: *"(8,6,4,8,6,4)" no axis of symmetry; chiral: *"(5,4,3,4,4,4) (0 1)(2 3)(4)(5)", "(3,4,4,4,4,4) (0 1)(2 3)(4)(5)" *"(5,3,4,4,3,3) (0 1)(2 4)(3)(5)", "(3,6,6,6,6,6) (0 1)(2 4)(3)(5)", "(4,4,3,3,3,3) (0 2)(1)(3 4)(5)", "(3,3,4,3,4,4) (0 4)(1)(2 3)(5)" *"(6,3,5,3,4,3) (0 1)(2 3)(4 5)", "(5,3,4,3,3,3) (0 1)(2 3)(4 5)" no axis of symmetry: *"(14,12,10,8,6,4)", "(6,6,4,6,4,4)", "(8,6,4,4,4,4)", "(8,4,6,4,4,4)", "(8,6,6,4,4,4)", "(8,6,4,6,4,4)", "(6,8,4,6,4,4)", "(8,4,6,6,4,4)", "(8,8,6,6,4,4)", "(8,6,8,6,4,4)", "(10,8,6,4,4,4)", "(10,8,4,6,4,4)", "(10,4,8,4,6,4)", "(10,8,6,6,4,4)", "(10,6,8,6,4,4)", "(6,10,8,6,4,4)", "(10,6,6,8,4,4)", "(10,8,6,4,6,4)", "(10,6,8,4,6,4)", "(10,6,4,8,6,4)", "(12,10,8,6,4,4)", "(12,10,8,4,6,4)", "(12,10,4,8,6,4)" *"(12,10,8,6,4,4) (5)", "(6,4,4,4,4,4) (4)", "(6,4,4,4,4,4) (5)", "(6,6,4,4,4,4) (5)", "(6,4,6,4,4,4) (5)", "(4,4,4,6,6,6) (1)", "(4,4,6,4,6,6) (1)", "(8,6,4,4,4,4) (4)", "(8,6,4,4,4,4) (5)", "(8,4,6,4,4,4) (5)", "(8,4,4,6,4,4) (5)", "(6,8,8,4,4,4) (2)", "(8,6,6,4,4,4) (5)", "(8,6,6,4,4,4) (4)", "(6,8,6,4,4,4) (5)", "(8,6,4,6,4,4) (5)", "(6,8,4,6,4,4) (5)", "(6,4,8,8,4,4) (3)", "(8,4,6,6,4,4) (5)", "(8,8,6,6,4,4) (1)", "(8,6,8,6,4,4) (5)", "(10,8,6,4,4,4) (5)", "(10,8,4,6,4,4) (5)", "(10,8,6,6,4,4) (5)", "(10,6,8,6,4,4) (5)", "(6,10,8,6,4,4) (5)", "(10,6,6,8,4,4) (5)" *"(10,8,4,6,6,6) (4)(5)", "(4,6,6,6,6,6) (4)(5)", "(4,4,6,6,6,6) (4)(5)", "(8,4,6,6,6,6) (4)(5)", "(8,6,4,6,6,6) (4)(5)", "(8,4,4,6,6,6) (4)(5)" *"(10,6,8,8,4,4) (3)(5)", "(6,4,4,4,4,4) (3)(5)", "(8,8,4,4,4,4) (1)(5)", "(8,8,8,4,4,4) (1)(5)", "(8,8,4,8,4,4) (1)(5)", "(8,6,4,4,4,4) (3)(5)", "(6,8,8,4,4,4) (2)(4)", "(6,4,8,8,4,4) (3)(5)", "(8,8,6,6,4,4) (1)(5)" *"(10,8,8,6,4,4) (2)(5)", "(8,8,8,4,4,4) (1)(4)", "(6,8,8,4,4,4) (2)(5)" *"(10,8,6,4,3,4) (4 5)", "(6,4,4,4,4,4) (4 5)", "(6,6,4,4,4,4) (4 5)", "(6,4,6,4,4,4) (0 1)", "(6,6,4,6,4,4) (3 4)", "(8,6,4,4,4,4) (4 5)", "(3,4,6,4,4,4) (0 1)", "(8,4,6,4,4,4) (4 5)", "(8,6,6,4,4,4) (4 5)", "(6,8,4,8,4,4) (2 3)", "(8,6,4,6,4,4) (3 4)", "(6,8,4,6,4,4) (3 4)", "(3,4,6,6,4,4) (0 1)", "(8,4,6,4,6,4) (4 5)", "(8,6,8,6,4,4) (1 2)", "(10,8,6,4,4,4) (4 5)", "(8,6,4,3,4,4) (3 4)", "(3,4,8,4,6,4) (0 1)", "(8,4,3,4,6,6) (2 3)", "(10,8,6,4,6,4) (4 5)", "(10,6,8,4,6,4) (4 5)" *"(8,10,6,8,4,4) (0 4)", "(6,4,4,4,4,4) (3 5)", "(8,8,4,8,4,4) (0 4)", "(8,6,4,4,4,4) (3 5)", "(8,6,4,8,4,4) (0 4)", "(6,4,8,8,4,4) (2 4)" *"(10,8,4,6,6,6) [4 5]", "(4,6,6,6,6,6) [4 5]", "(4,4,6,6,6,6) [4 5]", "(8,4,6,6,6,6) [4 5]", "(8,6,4,6,6,6) [4 5]", "(8,4,4,6,6,6) [4 5]" *"(10,6,8,4,8,4) [3 5]", "(6,4,4,4,4,4) [3 5]", "(8,4,8,4,4,4) [0 2]", "(8,8,4,8,4,4) [2 4]", "(8,6,4,4,4,4) [3 5]", "(6,8,4,8,4,4) [2 4]", "(6,4,8,4,8,4) [3 5]", "(8,4,8,4,6,6) [1 3]" *"(10,8,4,6,8,4) [2 5]", "(8,8,4,8,4,4) [0 3]", "(8,6,4,8,4,4) [0 3]" *"(6,4,8,8,8,8) (3)(4)(5)", "(4,8,8,8,8,8) (3)(4)(5)" *"(8,4,4,6,6,6) (2)(4)(5)", "(4,12,12,12,12,12) (2)(4)(5)", "(4,4,6,6,6,6) (1)(4)(5)", "(4,4,4,6,6,6) (1)(4)(5)" *"(12,12,8,8,4,4) (1)(3)(5)" *"(8,4,6,3,6,6) (3 4)(5)", "(3,6,6,6,6,6) (0 1)(5)", "(4,6,6,6,6,6) (3 4)(5)", "(4,6,6,6,6,6) (3)(4 5)", "(4,4,6,6,6,6) (3 4)(5)", "(4,6,4,6,6,6) (0 1)(5)", "(6,6,4,6,4,4) (1)(2 3)", "(8,4,6,6,6,6) (3 4)(5)", "(3,6,4,6,6,6) (0 1)(5)", "(4,6,6,3,6,6) (3 4)(5)", "(8,4,6,4,6,6) (3 4)(5)", "(4,8,6,4,6,6) (3 4)(5)", "(3,6,4,4,6,6) (0 1)(5)" *"(6,8,3,8,4,4) (2 3)(5)", "(3,4,4,4,4,4) (0 1)(4)", "(6,4,4,4,4,4) (2 3)(5)", "(8,8,4,4,4,4) (1)(4 5)", "(6,4,6,4,4,4) (0 1)(4)", "(8,4,8,4,4,4) (1 2)(5)", "(8,8,8,4,4,4) (1)(4 5)", "(8,8,4,8,4,4) (1)(3 4)", "(3,4,6,4,4,4) (0 1)(4)", "(6,8,8,4,4,4) (2)(4 5)", "(8,3,8,4,4,4) (1 2)(5)", "(6,8,4,8,4,4) (2 3)(5)", "(3,4,8,8,4,4) (0 1)(3)", "(8,6,8,6,4,4) (1 2)(5)" *"(4,10,8,4,6,6) (0 4)(5)", "(6,4,4,4,4,4) (3 5)(4)", "(4,4,6,4,6,6) (0 4)(5)", "(8,6,4,4,4,4) (3 5)(4)", "(8,6,4,8,4,4) (0 4)(5)", "(8,4,6,6,4,4) (2 4)(3)" *"(8,6,4,4,6,6) (2 4)(5)", "(4,12,12,12,12,12) (2 4)(5)", "(4,4,6,6,6,6) (0 2)(5)", "(6,6,4,6,4,4) (0 4)(1)" *"(4,8,4,6,6,6) (0 3)(5)", "(4,12,12,12,12,12) (2 5)(4)", "(4,6,4,6,6,6) (0 3)(5)", "(6,6,6,4,4,4) (0 3)(1)" *"(6,4,8,8,8,8) [3 4](5)", "(4,8,8,8,8,8) [3 4](5)", "(4,8,8,8,8,8) (3)[4 5]", "(4,4,8,8,8,8) [3 4](5)" *"(8,4,4,6,6,6) (2)[4 5]", "(4,12,12,12,12,12) [2 3](5)", "(4,4,6,6,6,6) (1)[4 5]", "(4,4,4,6,6,6) (1)[4 5]" *"(6,4,8,8,8,8) [3 5](4)", "(4,8,8,8,8,8) [3 5](4)" *"(8,4,6,4,6,6) [2 4](5)", "(4,12,12,12,12,12) [2 4](5)", "(4,6,4,6,6,6) [0 2](5)", "(6,6,4,6,4,4) (1)[2 4]" *"(12,8,12,8,4,4) [1 3](5)", "(8,4,8,4,4,4) [0 2](4)" *"(4,8,6,4,6,6) [0 3](5)", "(4,12,12,12,12,12) [2 5](4)", "(6,6,4,6,4,4) [0 3](1)" *"(3,6,4,4,6,6) (0 1)(3)(5)", "(3,12,12,12,12,12) (0 1)(3)(5)", "(4,4,6,6,6,6) (1)(3 4)(5)", "(4,4,6,4,6,6) (1)(3 4)(5)" *"(3,8,4,8,8,8) (0 1)(4)(5)", "(3,8,8,8,8,8) (0 1)(4)(5)", "(4,8,8,8,8,8) (2 3)(4)(5)", "(4,8,4,8,8,8) (0 1)(4)(5)" *"(8,6,4,4,6,6) (2 4)(3)(5)", "(4,6,6,6,6,6) (2 4)(3)(5)", "(4,4,6,6,6,6) (0 2)(1)(5)", "(6,6,4,6,4,4) (0 4)(1)(5)" *"(4,4,8,8,8,8) (0 2)(4)(5)" *"(12,12,12,6,6,6) (0 3)(1)(5)" *"(12,12,12,6,6,6) (0 3)(1)(4)" *"(4,10,10,10,10,10) [2 3](4)(5)" *"(4,4,8,8,8,8) (1)[3 4](5)" *"(4,10,10,10,10,10) [2 4](3)(5)" *"(12,12,6,12,6,6) (1)[2 4](5)" *"(12,12,6,12,6,6) [0 3](1)(5)" *"(5,6,4,6,3,6) (0 1)(4 5)", "(3,6,6,6,6,6) (0 1)(4 5)", "(4,6,4,6,6,6) (0 1)(4 5)", "(4,6,3,6,6,6) (0 1)(2 3)", "(3,6,4,6,6,6) (0 1)(4 5)", "(3,6,4,6,4,6) (0 1)(4 5)" *"(3,6,4,4,6,6) (0 1)(2 4)", "(3,12,12,12,12,12) (0 1)(3 5)", "(4,4,6,6,6,6) (0 2)(4 5)", "(6,6,4,6,4,4) (0 4)(2 3)" *"(3,8,4,8,8,8) (0 1)[4 5]", "(3,8,8,8,8,8) (0 1)[4 5]", "(4,8,8,8,8,8) [2 3](4 5)", "(4,8,4,8,8,8) (0 1)[4 5]" *"(3,6,4,6,4,6) (0 1)[3 5]", "(3,12,12,12,12,12) (0 1)[3 5]", "(4,6,4,6,6,6) [0 2](4 5)" *"(4,4,8,8,8,8) (0 2)[4 5]" *"(4,10,10,10,10,10) (2 4)[3 5]" *"(12,12,6,12,6,6) [0 3][2 4]" *"(3,10,10,10,10,10) (0 1)(2)(4)(5)" *"(3,10,10,10,10,10) (0 1)(3)(4)(5)" *"(4,4,8,8,8,8) (0 2)(1)(4)(5)" *"(6,6,6,3,3,3) (0 3)(1)(4)(5)" *"(4,8,3,8,8,8) (0 1)(2 3)(5)", "(3,8,8,8,8,8) (0 1)(3)(4 5)", "(3,8,8,8,8,8) (0 1)(2 3)(5)", "(3,8,3,8,8,8) (0 1)(2 3)(5)" *"(4,8,8,3,8,8) (0 1)(3 4)(5)", "(3,8,8,8,8,8) (0 1)(3 4)(5)" *"(5,3,4,4,3,3) (0 1)(2 4)(5)", "(3,12,12,12,12,12) (0 1)(2 4)(5)", "(4,4,3,3,3,3) (0 2)(3 4)(5)", "(3,3,4,3,4,4) (0 4)(1)(2 3)" *"(3,6,4,4,6,6) (0 1)(2 4)(3)", "(3,6,6,6,6,6) (0 1)(3 5)(4)", "(4,4,6,6,6,6) (0 2)(1)(4 5)", "(6,6,4,6,4,4) (0 4)(2 3)(5)" *"(4,3,4,6,6,6) (0 3)(1 2)(5)", "(3,6,6,6,6,6) (0 1)(2 5)(4)", "(4,6,4,6,6,6) (0 3)(1 2)(5)", "(6,6,6,4,4,4) (0 3)(1)(4 5)" *"(3,10,10,10,10,10) (0 1)[2 3](5)" *"(3,10,10,10,10,10) (0 1)(3)[4 5]" *"(3,10,10,10,10,10) (0 1)[3 4](5)" *"(3,10,10,10,10,10) (0 1)[2 4](5)" *"(3,10,10,10,10,10) (0 1)[3 5](4)" *"(3,10,10,10,10,10) (0 1)[2 5](4)" *"(4,4,8,8,8,8) (0 2)(1)[4 5]" *"(8,8,4,4,4,4) (0 2)[3 4](5)" *"(6,6,6,3,3,3) (0 3)(1)[4 5]" *"(4,8,4,8,8,8) [0 2][1 3](5)" *"(3,3,6,3,6,6) [0 3](1)[2 4]" *"(3,5,5,5,5,5) (0 1)[2 3](4)(5)" *"(3,5,5,5,5,5) (0 1)[2 4](3)(5)" *"(6,6,4,4,4,4) (0 2)(1)[3 4](5)" *"(5,4,3,4,4,4) (0 1)(2 3)[4 5]", "(3,4,4,4,4,4) (0 1)[2 3](4 5)" *"(3,5,5,5,5,5) (0 1)(2 4)[3 5]" *"(6,6,3,6,3,3) [0 3](1)[2 4](5)"