1、32 crystallographic point gropsWith Gif AnimationsThe 32 crystallographisics4.http:/en.wikipedia.org/wiki/Crystal_system5.http:/en.wikipedia.org/wiki/Space_group。
2、c point groups(point groups consistent with translational symmetry)32 Poals.cmu.edu/degraef/pg/pg.html3.G.Burns,Space Groups for Solid State Phy。
3、int groups can be constructed From 11 initial pure rotational point grouin 3Dreferences1.Lecture Notes,The Univ.of Texas at Austin2.http:/materi。
4、ps inversion centers can be added to produce an additional 11 centrosymmry14 Bravais lattice types into 7 lattice systems Table of space groups 。
5、etric point groups From the centrosymmetric point groups an additional 17 lattice systemsFlowchart for Determining SignificantPoint Group Symmet。
6、0 symmetries can be discoveredCyclic Point GroupsSym.Elem.Sym.Elem.Sym.Em.Sym.Elem.O GroupsSym.Elem.Sym.Elem.crystallographic Point groups into 。
7、lem.Sym.Elem.Sym.Elem.Cyclic+Horizontal Mirror GroupsSym.Elem.Sym.Elem.SCombination with no Unique AxisT GroupsO GroupsT GroupsSym.Elem.Sym.Ele。
8、ym.Elem.Sym.Elem.Sym.Elem.Cyclic+Vertical Mirror GroupsSym.Elem.Sym.ElemElem.Sym.Elem.Dihedral Groups+sdSym.Elem.Sym.Elem.Isometric Groups Roto。
9、Sym.Elem.Sym.Elem.Rotoreflection GroupsSym.Elem.Sym.Elem.Sym.Ebination Elem.Sym.Elem.Sym.Elem.Sym.Elem.Dihedral Groups+shSym.Elem.Sym.Elem.Sym。
10、of rotations with other rotations in other directionsAllowed Combinations of Pure Rotations：Rotations+Perpendicular 2-foldsDihedral(Dn)GroupsSym。
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