symmetry elements and crystallographic axes

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7 Terms

1
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triclinic

Primary Symmetry elements: none or inversion center (1-fold)

Relation to crystallographic axes: No symmetry aligned with axes a, b, and c

2
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monoclinic

Primary Symmetry elements: 1 mirror plane or 1 2-fold axes

Relation to crystallographic axes: 2-fold axis or mirror plane aligned with b-axis

3
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orthorhombic

Primary Symmetry elements: three 2-fold axes or three mirror planes

Relation to crystallographic axes: 2-fold axes parallel to a, b and c

4
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tetragonal

Primary Symmetry elements: 1 4-fold axis, possibly with 2-fold axes

Relation to crystallographic axes: 4-fold axis aligned with c=axis, a and b equal

5
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hexagonal

Primary Symmetry elements: 1 6-fold axis, possibly with mirror planes

Relation to crystallographic axes: 6-fold axis along c; a1, a2, a3 in basal plane

6
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trigonal

Primary Symmetry elements: 1 3-fold axis

Relation to crystallographic axes: 3-fold axis aligned with c; axes in basal plane

7
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cubic/ isometric

Primary Symmetry elements: four 3-fold axes, several 4-fold axes, mirror planes

Relation to crystallographic axes: 4-fold axes parallel to a, b, and c