Question

Let o and 7 be the following symmetries of the regular pentagon: 2. 2 240° rotation o reflection т 5 6 6 (a) (6 points) Express o and 7 as permutations of the vertices (i.e., in two-row notation). (b) (9 points) Compute the following permutations. Express answers in two-row notation. i. OOT ii. Too iii. TOOOT (c) (5 points) Determine the symmetry represented by TOOOT. Give the axis of symmetry if a reflection, or the degrees of clock-wise rotation if a rotation.

Answer 1

- 2 6 २ 240° grotection reflection 3 5 । ट 4 (4) । 2 3 4 5 6 3 4 5 6 । ५ 56 ८. i) 2 3 २ । 6 5 4 3/ (b) 601 1 2 3 4 56 3 4 5 6 )2 । 2 3 456 २ । 6 5 4 3 । ( . 2 3 4 5 6 432 । 65 6) 23466 3 4 5 6 । २ %3D (३२३.५.६६)(31 (13३५६१) 5) ToGoT = । 2 3 5 २। 6 5 4 3 4 45/1/1234561 615)(216543) । 2 3 4 56 56 1 2 3 4 (c) 5 १ rotation ५ 6 5 3 २०० ५ 3 २ Thus T0607 18 २०० rotation. CScanned with CamScanner