▁blue ) ▁have ▁point ▁symmetry , ▁also ▁known ▁as ▁rot ational ▁symmetry ▁of ▁order ▁ 2 . ▁Their ▁symmetry ▁group ▁has ▁two ▁elements , ▁the ▁identity ▁and ▁the ▁ 1 8 0 ° ▁rotation . ▁▁ 3 ▁he pt om ino es ▁( col oured ▁pur ple ) ▁have ▁two ▁axes ▁of ▁reflection ▁symmetry , ▁both ▁aligned ▁with ▁the ▁grid lines . ▁Their ▁symmetry ▁group ▁has ▁four ▁elements , ▁the ▁identity , ▁two ▁ref lections ▁and ▁the ▁ 1 8 0 ° ▁rotation . ▁It ▁is ▁the ▁di hed ral ▁group ▁of ▁order ▁ 2 , ▁also ▁known ▁as ▁the ▁Klein ▁four - group . ▁ 1 ▁he pt om ino ▁( col oured ▁orange ) ▁has ▁two ▁axes ▁of ▁reflection ▁symmetry , ▁both ▁aligned ▁with ▁the ▁diag on als . ▁Its ▁symmetry ▁group ▁also ▁has ▁four ▁elements . ▁Its ▁symmetry ▁group ▁is ▁also ▁the ▁di hed ral ▁group ▁of ▁order ▁ 2 ▁with ▁four ▁elements . ▁ ▁If ▁ref lections ▁of ▁a ▁he pt om ino ▁are ▁considered ▁distinct , ▁as ▁they ▁are ▁with ▁one - s ided ▁he pt om ino es , ▁then ▁the ▁first ▁and ▁fourth ▁categories ▁above ▁would ▁each ▁double ▁in ▁size , ▁resulting ▁in ▁an ▁extra ▁ 8 8 ▁he pt om ino es ▁for ▁a ▁total ▁of ▁ 1 9 6 . ▁If ▁rot ations ▁are ▁also ▁considered ▁distinct , ▁then ▁the ▁he pt om ino es ▁from ▁the ▁first ▁category ▁count ▁eight fold , ▁the ▁ones ▁from ▁the ▁next ▁three ▁categories ▁count ▁four fold ,