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1、32 crystallographic point gropsWith Gif Animations,The 32 crystallographic point groups(point groups consistent with translational symmetry),32 Point groups can be constructed,From 11 initial pure rotational point groupsinversion centers can be added to produce an additional 11 centrosymmetric point
2、 groupsFrom the centrosymmetric point groups an additional 10 symmetries can be discovered,Cyclic Point Groups,Sym.Elem.,Sym.Elem.,Sym.Elem.,Sym.Elem.,Sym.Elem.,Cyclic+Horizontal Mirror Groups,Sym.Elem.,Sym.Elem.,Sym.Elem.,Sym.Elem.,Sym.Elem.,Cyclic+Vertical Mirror Groups,Sym.Elem.,Sym.Elem.,Sym.Ele
3、m.,Sym.Elem.,Rotoreflection Groups,Sym.Elem.,Sym.Elem.,Sym.Elem.,combination of rotations with other rotations in other directions,Allowed Combinations of Pure Rotations：,Rotations+Perpendicular 2-foldsDihedral(Dn)Groups,Sym.Elem.,Sym.Elem.,Sym.Elem.,Sym.Elem.,Dihedral Groups+sh,Sym.Elem.,Sym.Elem.,
4、Sym.Elem.,Sym.Elem.,Dihedral Groups+sd,Sym.Elem.,Sym.Elem.,Isometric Groups Roto-Combination with no Unique Axis,T Groups,O Groups,T Groups,Sym.Elem.,Sym.Elem.,Sym.Elem.,O Groups,Sym.Elem.,Sym.Elem.,crystallographic Point groups into 7 lattice systems,Flowchart for Determining SignificantPoint Group
5、 Symmetry,14 Bravais lattice types into 7 lattice systems,Table of space groups in 3D,references,Lecture Notes,The Univ.of Texas at Austinhttp:/materials.cmu.edu/degraef/pg/pg.htmlG.Burns,Space Groups for Solid State Physicshttp:/en.wikipedia.org/wiki/Crystal_systemhttp:/en.wikipedia.org/wiki/Space_group,
