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Crystallography

Gypsum Monoclinic

Dolomite Triclinic

Emerald Hexagonal

 AndalusiteOrthorhombic

Garnet Isometric

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Symmetry Symbols Reflection (m)! produced by a mirror

plane that passes through a crystalstructure so the pattern on one side is amirror image o" the pattern on the other#

$symmetry o%er a plane&

 ' Ho( many mirror planes

do these crystals ha%e)

*oth ha%e +,

So notation is +m

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Rotation (A)! rotational symmetry in%ol%esrepeating a moti" by a set o" uni"orm rotationsaround an axis# $symmetry about an axis& ' -epeating the pattern e%ery ./01 o" rotation means +!

"old symmetry#

 ' E%ery 201 3 2!"old symmetry

 ' Denoted as 4Ax

(here x3x "old rotational symmetry

Orthorhombic! + axes o" /!"old symmetry5 so

notation is +A/

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More rotation

examples

(((#tulane#edu67sanelson

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In%ersion $i&! also 8no(n as centersymmetry# Any line dra(n through the

origin (ill "ind identical "eaturese9uidistant "rom the origin on the oppositeside#

*oth o" these crystals ha%e center symmetry $i&

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-otoin%ersion $:x& ! in%ol%es a rotation andin%ersion to repeat a pattern

 ' Denoted as 4:x (here x3x "old rotationalsymmetry

 ' ;ote :. 3 i and :/ 3 m

im +:+

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The +/ crystal classes represent the +/possible combinations o" symmetryoperations#

Each crystal class (ill ha%e crystal "acesthat uni9uely de"ine the symmetry o" theclass#

These "aces5 or groups o" "aces are calledcrystal "orms# 

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;ote that the +/ crystal classes aredi%ided into 2 crystal systems#

The Triclinic System has only .!"old or .!"old rotoin%ersion axes#

The Monoclinic System has only mirrorplane$s& or a single /!"old axis#

The Orthorhombic System has only t(o"old axes or a /!"old axis and / mirrorplanes#

The Tetragonal System has either asingle <!"old or <!"old rotoin%ersion axis#

The Hexagonal System has no <!"oldaxes5 but has at least . 2!"old or +!"oldaxis#

The Isometric System has either < +!"oldaxes or < +!"old rotoin%ersion axes#

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Symmetry Operation Symmetry Symbol Hermann!Mauguin Symbol

Mirror m m

-otation A.5A/5A+5A<5A2 .5/5+5<52 Axis

-otoin%ersion :.3i5 :/5:+5:<5:2 .5/5+5<52

 Axis

!! ! ! !

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Miller Indices

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Miller Indices

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Created by ;icolas *arth/00=

Geology ..<*>ni%ersity o" Cali"ornia5 Santa *arbaraSome images herein borro(ed "rom

(ebsites ha%e not been credited