I was looking for the operation table for the symmetries of a equilateral triangle. I have found this webpage:
http://members.tripod.com/~dogschool/trianglegroup.html
-
e stand for the Do nothing movement.
-
a stand for the Rotate 120 degrees counterclockwise
movement.
-
b stand for the Rotate 240 degrees counterclockwise
movement.
-
X stand for the Flip about axis through the top vertex
movement.
-
Y stand for the Flip about the axis through the lower-left
vertex movement.
-
Z stand for the Flip about the axis through the lower-right
vertex movement.
| • |
e |
a |
b |
X |
Y |
Z |
| e |
e |
a |
b |
X |
Y |
Z |
| a |
a |
b |
e |
Y |
Z |
X |
| b |
b |
e |
a |
Z |
X |
Y |
| X |
X |
Z |
Y |
e |
b |
a |
| Y |
Y |
X |
Z |
a |
e |
b |
| Z |
Z |
Y |
X |
b |
a |
e |