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List of the 230 crystallographic 3D space groups



Contents

Triclinic system

Class # Space groups
1\,\! 1 \mathrm{P}1\,\!
\bar{1} 2 \mathrm{P}\bar{1}

Monoclinic system

Class # Space groups
2\,\! 3-5 \mathrm{P}2\,\! \mathrm{P}2_{1}\,\! \mathrm{C}2\,\!  
\mathrm{m}\,\! 6-9 \mathrm{Pm}\,\! \mathrm{Pc}\,\! \mathrm{Cm}\,\! \mathrm{Cc}\,\!
2/m\,\! 10-15 \mathrm{P}2/\mathrm{m}\,\! \mathrm{P}2_{1}/\mathrm{m}\,\! \mathrm{C}2/\mathrm{m}\,\! \mathrm{P}2/\mathrm{c}\,\!
\mathrm{P}2_{1}/\mathrm{c}\,\! \mathrm{C}2/\mathrm{c}\,\!  

Orthorhombic system

Class # Space groups
222\,\! 16-24 \mathrm{P}222\,\! \mathrm{P}222_{1}\,\! \mathrm{P}2_{1}2_{1}2\,\! \mathrm{P}2_{1}2_{1}2_{1}\,\! \mathrm{C}222_{1}\,\! \mathrm{C}222\,\! \mathrm{F}222\,\! \mathrm{I}222\,\!
\mathrm{I}2_{1}2_{1}2_{1}\,\!  
\mathrm{mm}2\,\! 25-46 \mathrm{Pmm}2\,\! \mathrm{Pmc}2_{1}\,\! \mathrm{Pcc}2\,\! \mathrm{Pma}2\,\! \mathrm{Pca}2_{1}\,\! \mathrm{Pnc}2\,\! \mathrm{Pmn}2_{1}\,\! \mathrm{Pba}2\,\!
\mathrm{Pna}2_{1}\,\! \mathrm{Pnn}2\,\! \mathrm{Cmm}2\,\! \mathrm{Cmc}2_{1}\,\! \mathrm{Ccc}2\,\! \mathrm{Amm}2\,\! \mathrm{Aem}2\,\! \mathrm{Ama}2\,\!
\mathrm{Aea}2\,\! \mathrm{Fmm}2\,\! \mathrm{Fdd}2\,\! \mathrm{Imm}2\,\! \mathrm{Iba}2\,\! \mathrm{Ima}2\,\!  
\mathrm{mmm}\,\! 47-74 \mathrm{Pmmm}\,\! \mathrm{Pnnn}\,\! \mathrm{Pccm}\,\! \mathrm{Pban}\,\! \mathrm{Pmma}\,\! \mathrm{Pnna}\,\! \mathrm{Pmna}\,\! \mathrm{Pcca}\,\!
\mathrm{Pbam}\,\! \mathrm{Pccn}\,\! \mathrm{Pbcm}\,\! \mathrm{Pnnm}\,\! \mathrm{Pmmn}\,\! \mathrm{Pbcn}\,\! \mathrm{Pbca}\,\! \mathrm{Pnma}\,\!
\mathrm{Cmcm}\,\! \mathrm{Cmce}\,\! \mathrm{Cmmm}\,\! \mathrm{Cccm}\,\! \mathrm{Cmme}\,\! \mathrm{Ccce}\,\! \mathrm{Fmmm}\,\! \mathrm{Fddd}\,\!
\mathrm{Immm}\,\! \mathrm{Ibam}\,\! \mathrm{Ibca}\,\! \mathrm{Imma}\,\!  

Note. An e plane is a double glide plane, one having glides in two different directions. They are found in five space groups, all in the orthorhombic system and with a centered lattice. The use of the symbol e became official with the 5th edition of the International tables for crystallography, volume A (2002).

Tetragonal system

Class # Space groups
4\,\! 75-80 \mathrm{P}4\,\! \mathrm{P}4_{1}\,\! \mathrm{P}4_{2}\,\! \mathrm{P}4_{3}\,\! \mathrm{I}4\,\! \mathrm{I}4_{1}\,\!
\bar{4}\,\! 81-82 \mathrm{P}\bar{4}\,\! \mathrm{I}\bar{4}\,\!  
\bar{4}/\mathrm{m}\,\! 83-88 \mathrm{P}4/\mathrm{m}\,\! \mathrm{P}4_{2}/\mathrm{m}\,\! \mathrm{P}4/\mathrm{n}\,\! \mathrm{P}4_{2}/\mathrm{n}\,\! \mathrm{I}4/\mathrm{m}\,\! \mathrm{I}4_{1}/\mathrm{a}\,\!
422\,\! 89-98 \mathrm{P}422\,\! \mathrm{P}42_{1}2\,\! \mathrm{P}4_{1}22\,\! \mathrm{P}4_{1}2_{1}2\,\! \mathrm{P}4_{2}22\,\! \mathrm{P}4_{2}2_{1}2\,\!
\mathrm{P}4_{3}22\,\! \mathrm{P}4_{3}2_{1}2\,\! \mathrm{I}422\,\! \mathrm{I}4_{1}22\,\!  
4\mathrm{mm}\,\! 99-110 \mathrm{P}4\mathrm{mm}\,\! \mathrm{P}4\mathrm{bm}\,\! \mathrm{P}4_{2}\mathrm{cm}\,\! \mathrm{P}4_{2}\mathrm{nm}\,\! \mathrm{P}4\mathrm{cc}\,\! \mathrm{P}4\mathrm{nc}\,\!
\mathrm{P}4_{2}\mathrm{mc}\,\! \mathrm{P}4_{2}\mathrm{bc}\,\! \mathrm{I}4\mathrm{mm}\,\! \mathrm{I}4\mathrm{cm}\,\! \mathrm{I}4_{1}\mathrm{md}\,\! \mathrm{I}4_{1}\mathrm{cd}\,\!
\bar{4}2\mathrm{m}\,\! 111-122 \mathrm{P}\bar{4}2\mathrm{m}\,\! \mathrm{P}\bar{4}2\mathrm{c}\,\! \mathrm{P}\bar{4}2_{1}\mathrm{m}\,\! \mathrm{P}\bar{4}2_{1}\mathrm{c}\,\! \mathrm{P}\bar{4}\mathrm{m}2\,\! \mathrm{P}\bar{4}\mathrm{c}2\,\!
\mathrm{P}\bar{4}\mathrm{b}2\,\! \mathrm{P}\bar{4}\mathrm{n}2\,\! \mathrm{I}\bar{4}\mathrm{m}2\,\! \mathrm{I}\bar{4}\mathrm{c}2\,\! \mathrm{I}\bar{4}2\mathrm{m}\,\! \mathrm{I}\bar{4}2\mathrm{d}\,\!
4/\mathrm{mmm}\,\! 123-142 \mathrm{P}4/\mathrm{mmm}\,\! \mathrm{P}4/\mathrm{mmc}\,\! \mathrm{P}4/\mathrm{nbm}\,\! \mathrm{P}4/\mathrm{nnc}\,\! \mathrm{P}4/\mathrm{mbm}\,\! \mathrm{P}4/\mathrm{mnc}\,\!
\mathrm{P}4/\mathrm{nmm}\,\! \mathrm{P}4/\mathrm{ncc}\,\! \mathrm{P}4_{2}/\mathrm{mmc}\,\! \mathrm{P}4_{2}/\mathrm{mcm}\,\! \mathrm{P}4_{2}/\mathrm{nbc}\,\! \mathrm{P}4_{2}/\mathrm{nnm}\,\!
\mathrm{P}4_{2}/\mathrm{mbc}\,\! \mathrm{P}4_{2}/\mathrm{mnm}\,\! \mathrm{P}4_{2}/\mathrm{nmc}\,\! \mathrm{P}4_{2}/\mathrm{ncm}\,\! \mathrm{I}4/\mathrm{mmm}\,\! \mathrm{I}4/\mathrm{mcm}\,\!
\mathrm{I}4_{1}/\mathrm{amd}\,\! \mathrm{I}4_{1}/\mathrm{acd}\,\!  

Rhombohedral (trigonal) system

Class # Space groups
3\,\! 143-146 \mathrm{P}3\,\! \mathrm{P}3_{1}\,\! \mathrm{P}3_{2}\,\! \mathrm{R}3\,\!  
\bar{3}\,\! 147-148 \mathrm{P}\bar{3}\,\! \mathrm{R}\bar{3}\,\!  
32\,\! 149-155 \mathrm{P}312\,\! \mathrm{P}321\,\! \mathrm{P}3_{1}12\,\! \mathrm{P}3_{1}21\,\! \mathrm{P}3_{2}12\,\! \mathrm{P}3_{2}21\,\! \mathrm{R}32\,\!
3\mathrm{m}\,\! 156-161 \mathrm{P}3\mathrm{m}1\,\! \mathrm{P}31\mathrm{m}\,\! \mathrm{P}3\mathrm{c}1\,\! \mathrm{P}31\mathrm{c}\,\! \mathrm{R}3\mathrm{m}\,\! \mathrm{R}3\mathrm{c}\,\!  
\bar{3}\mathrm{m} 162-167 \mathrm{P}\bar{3}1\mathrm{m}\,\! \mathrm{P}\bar{3}1\mathrm{c}\,\! \mathrm{P}\bar{3}\mathrm{m}1\,\! \mathrm{P}\bar{3}\mathrm{c}1\,\! \mathrm{R}\bar{3}\mathrm{m}\,\! \mathrm{R}\bar{3}\mathrm{c}\,\!  

Hexagonal system

Class # Space groups
6\,\! 168-173 \mathrm{P}6\,\! \mathrm{P}6_{1}\,\! \mathrm{P}6_{5}\,\! \mathrm{P}6_{2}\,\! \mathrm{P}6_{4}\,\! \mathrm{P}6_{3}\,\!
\bar{6}\,\! 174 \mathrm{P}\bar{6}\,\!  
6/\mathrm{m}\,\! 175-176 \mathrm{P}6/\mathrm{m}\,\! \mathrm{P}6_{3}/\mathrm{m}\,\!  
622\,\! 177-182 \mathrm{P}622\,\! \mathrm{P}6_{1}22\,\! \mathrm{P}6_{5}22\,\! \mathrm{P}6_{2}22\,\! \mathrm{P}6_{4}22\,\! \mathrm{P}6_{3}22\,\!
6\mathrm{mm}\,\! 183-186 \mathrm{P}6\mathrm{mm}\,\! \mathrm{P}6\mathrm{cc}\,\! \mathrm{P}6_{3}\mathrm{cm}\,\! \mathrm{P}6_{3}\mathrm{mc}\,\!  
\bar{6}\mathrm{m}2\,\! 187-190 \mathrm{P}\bar{6}\mathrm{m}2\,\! \mathrm{P}\bar{6}\mathrm{c}2\,\! \mathrm{P}\bar{6}2\mathrm{m}\,\! \mathrm{P}\bar{6}2\mathrm{c}\,\!  
6/\mathrm{mmm}\,\! 191-194 \mathrm{P}6/\mathrm{mmm}\,\! \mathrm{P}6/\mathrm{mcc}\,\! \mathrm{P}6_{3}/\mathrm{mcm}\,\! \mathrm{P}6_{3}/\mathrm{mmc}\,\!  

Cubic system

Class # Space groups
23\,\! 195-199 \mathrm{P}23\,\! \mathrm{F}23\,\! \mathrm{I}23\,\! \mathrm{P}2_{1}3\,\! \mathrm{I}2_{1}3\,\!  
\mathrm{m}\bar{3}\,\! 200-206 \mathrm{Pm}\bar{3}\,\! \mathrm{Pn}\bar{3}\,\! \mathrm{Fm}\bar{3}\,\! \mathrm{Fd}\bar{3}\,\! \mathrm{I}\bar{3}\,\! \mathrm{Pa}\bar{3}\,\! \mathrm{Ia}\bar{3}\,\!  
432\,\! 207-214 \mathrm{P}432\,\! \mathrm{P}4_{2}32\,\! \mathrm{F}432\,\! \mathrm{F}4_{1}32\,\! \mathrm{I}432\,\! \mathrm{P}4_{3}32\,\! \mathrm{P}4_{1}32\,\! \mathrm{I}4_{1}32\,\!
\bar{4}3\mathrm{m}\,\! 215-220 \mathrm{P}\bar{4}3\mathrm{m}\,\! \mathrm{F}\bar{4}3\mathrm{m}\,\! \mathrm{I}\bar{4}3\mathrm{m}\,\! \mathrm{P}\bar{4}3\mathrm{n}\,\! \mathrm{F}\bar{4}3\mathrm{c}\,\! \mathrm{I}\bar{4}3\mathrm{d}\,\!  
\mathrm{m}\bar{3}\mathrm{m}\,\! 221-230 \mathrm{Pm}\bar{3}\mathrm{m}\,\! \mathrm{Pn}\bar{3}\mathrm{n}\,\! \mathrm{Pm}\bar{3}\mathrm{n}\,\! \mathrm{Pn}\bar{3}\mathrm{m}\,\! \mathrm{Fm}\bar{3}\mathrm{m}\,\! \mathrm{Fm}\bar{3}\mathrm{c}\,\! \mathrm{Fd}\bar{3}\mathrm{m}\,\! \mathrm{Fd}\bar{3}\mathrm{c}\,\!
\mathrm{Im}\bar{3}\mathrm{m}\,\! \mathrm{Ia}\bar{3}\mathrm{d}\,\!  

See also

 
This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "List_of_the_230_crystallographic_3D_space_groups". A list of authors is available in Wikipedia.
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