7 ▁equal - s ized ▁squares ▁connected ▁edge - to - edge . ▁The ▁name ▁of ▁this ▁type ▁of ▁figure ▁is ▁formed ▁with ▁the ▁prefix ▁he pt ( a )- . ▁When ▁rot ations ▁and ▁ref lections ▁are ▁not ▁considered ▁to ▁be ▁distinct ▁shapes , ▁there ▁are ▁ 1 0 8 ▁different ▁free ▁he pt om ino es . ▁When ▁ref lections ▁are ▁considered ▁distinct , ▁there ▁are ▁ 1 9 6 ▁one - s ided ▁he pt om ino es . ▁When ▁rot ations ▁are ▁also ▁considered ▁distinct , ▁there ▁are ▁ 7 6 0 ▁fixed ▁he pt om ino es . ▁ ▁Sym met ry ▁The ▁figure ▁shows ▁all ▁possible ▁free ▁he pt om ino es , ▁col oured ▁according ▁to ▁their ▁symmetry ▁groups : ▁▁ 8 4 ▁he pt om ino es ▁( col oured ▁grey ) ▁have ▁no ▁symmetry . ▁Their ▁symmetry ▁group ▁consists ▁only ▁of ▁the ▁identity ▁mapping . ▁ 9 ▁he pt om ino es ▁( col oured ▁red ) ▁have ▁an ▁axis ▁of ▁reflection ▁symmetry ▁aligned ▁with ▁the ▁grid lines . ▁Their ▁symmetry ▁group ▁has ▁two ▁elements , ▁the ▁identity ▁and ▁the ▁reflection ▁in ▁a ▁line ▁parallel ▁to ▁the ▁sides ▁of ▁the ▁squares . ▁▁ 7 ▁he pt om ino es ▁( col oured ▁green ) ▁have ▁an ▁axis ▁of ▁reflection ▁symmetry ▁at ▁ 4 5 ° ▁to ▁the ▁grid lines . ▁Their ▁symmetry ▁group ▁has ▁two ▁elements , ▁the ▁identity ▁and ▁a ▁diagonal ▁reflection . ▁▁ 4 ▁he pt om ino es ▁( col oured