32晶体点群图示

32crystallographicpointgropsWithGifAnimationsThe32crystallographicpointgroups(pointgroupsconsistentwithtranslationalsymmetry)32Pointgroupscanbeconstructed•From11initialpurerotationalpointgroups•inversioncenterscanbeaddedtoproduceanadditional11centrosymmetricpointgroups•Fromthecentrosymmetricpointgroupsanadditional10symmetriescanbediscoveredCyclicPointGroups11C22C33C44C66C11CSym.Elem.22CSym.Elem.33CSym.Elem.44CSym.Elem.66CSym.Elem.Cyclic+HorizontalMirrorGroupshCm1hCm22hCm33hCm44hCm661hmCvCm1Sym.Elem.22hCmSym.Elem.33hCm36SSym.Elem.44hCmSym.Elem.66hCmSym.Elem.Cyclic+VerticalMirrorGroupsvCm1vCmm22vCm33vCmm44vCmm66hCm122vmmCSym.Elem.33vmCSym.Elem.44vmmCSym.Elem.66vmmCSym.Elem.RotoreflectionGroups21S44S63ShCm1hCm3312S36S21SSym.Elem.44SSym.Elem.63SSym.Elem.combinationofrotationswithotherrotationsinotherdirectionsAllowedCombinationsofPureRotations：Rotations+Perpendicular2-foldsDihedral(Dn)Groups2222D332D4422D6622D2222DSym.Elem.332DSym.Elem.4422DSym.Elem.6622DSym.Elem.DihedralGroups+shhDmmm2hDm326hDmmm44hDmmm662hmmmDSym.Elem.362hmDSym.Elem.44hmmDmSym.Elem.66hmmDmSym.Elem.DihedralGroups+sddDm224dDm33?4dD?6dDm28m212242dmDSym.Elem.33dmDSym.Elem.IsometricGroupsRoto-CombinationwithnoUniqueAxisTGroupsOGroupsTGroupsT23hTm3dTm3423TSym.Elem.3hmTSym.Elem.43dmTSym.Elem.OGroupsO432hOmm3432OSym.Elem.3hmmOSym.Elem.crystallographicPointgroupsinto7latticesystemsFlowchartforDeterminingSignificantPointGroupSymmetry14Bravaislatticetypesinto7latticesystemsTableofspacegroupsin3Dreferences1.LectureNotes,TheUniv.ofTexasatAustin2.://en.wikipedia.org/wiki/Crystal_system5.