New notation symbols for space groups,
point groups and crystal systems
The "Uniform ASCII symbols for space groups, point groups, and crystal systems" was presented at the 17th General Meeting of the International Mineralogical Association, Toronto, Canada, Aug. 9 - 14, 1998 by Doctor
Peter Susse.
The use of subscript and superscript characters in space group and point group symbols is quite disadvantageous for printing as well as for electronic data processing. While preparing the 6th edition of the mineral database MINABS , new symbols were designed consisting of a string of 5 ASCII characters for SCHOENFLIES style, and of up to 7 characters for the symbols after HERMANN-MAUGUIN. It proved to be very useful to extend the new symbols to crystal systems as well.
The symbol for the crystal system is made taking the SCHOENFLIES symbol of the holoedric point group, bringing the subscript characters in line, and filling the remainder of the 5 spaces with asterisks (ASCII 42), while in the point group symbol the remaining spaces are filled with periods (ASCII 46). The space group symbol is made adding the superscript number of SCHOENFLIES.
The ASCII format for the HERMANN-MAUGUIN style symbols is achieved by denoting inversion axes with the tilde " ~ " character (ASCII 126). The neutral screw axes 21, 42, and 63 are indicated by an apostrophe " ' "
(ASCII 39), while the (right handed) screw axes 31, 41, and 61 are indicated
by a right bracket " ] " (ASCII 93), or by a right brace " } " (ASCII 125) in case of 62. The (left handed) screw axes 32, 43, and 65 are denoted using the left bracket " [ " (ASCII 91), or the left brace " { " (ASCII 123) in case of 64.
For retrieving purposes in databases, the SCHOENFLIES symbols are useful because of their hierarchical nature and of being independent of crystal settings. The advantage of HERMANN- MAUGUIN symbols is the orientational information they contain. The combination of both, using the new ASCII symbols, is being successfully applied in the database MINABS.
If you require more information on this new notation, you may contact
Dr Peter Susse or visit his website.
| ci*** | triclinic |
| c2h** | monoclinic |
| d2h** | orthorhombic |
| d4h** | tetragonal |
| d3d** | trigonal |
| d6h** | hexagonal |
| oh*** | isometric |
Left column - new symbol Schoenflies type
Right column - Hermann-Mauguin type
|
|
| 1st column | - Space group |
| 2nd column | - New symbol Schoenflies type |
| 3rd column | - New symbol Hermann-Mauguin type |
| 4th column | - Other Orientations |
| Space | Sch. type | H-M type | Other |
| 1 - | c1..1 | P1 | |
| 2 - | ci... | 1 | P1~ |
| 3 - | c2... | 1 | P2 B2 |
| 4 - | c2..2 | P2' | B2' |
| 5 - | c2..3 | C2 | A2 I2 F2 |
| 6 - | cs..1 | Pm | Bm |
| 7 - | cs..2 | Pc | Pa Pn Bd |
| 8 - | cs..3 | Cm | Am Im Fm |
| 9 - | cs..4 | Cc | Aa Ia Fd |
| 10 - | c2h.1 | P2/m | B2/m |
| 11 - | c2h.2 | P2'/m | B2'/m |
| 12 - | c2h.3 | C2/m | A2/m I2/m F2/m |
| 13 - | c2h.4 | P2/c | P2/a P2/n B2/d |
| 14 - | c2h.5 | P2'/c | P2'/a P2'/n B2'/d |
| 15 - | c2h.6 | C2/c | A2/a I2/a F2/d |
| 16 - | d2..1 | P222 | |
| 17 - | d2..2 | P222' | P2'22 P22'2 |
| 18 - | d2..3 | P2'2'2 | P22'2' P2'22' |
| 19 - | d2..4 | P2'2'2' | |
| 20 - | d2..5 | C222' | A2'22 B22'2 |
| 21 - | d2..6 | C222 | A222 B222 |
| 22 - | d2..7 | F222 | |
| 23 - | d2..8 | I222 | |
| 24 - | d2..9 | I2'2'2' | |
| 25 - | c2v.1 | Pmm2 | P2mm Pm2m |
| 26 - | c2v.2 | Pmc2' | P2'ma Pb2'm Pm2'b Pcm2' P2'am |
| 27 - | c2v.3 | Pcc2 | P2aa Pb2b |
| 28 - | c2v.4 | Pma2 | P2mb Pc2m Pm2a Pbm2 P2cm |
| 29 - | c2v.5 | Pca2' | P2'ab Pc2'b Pb2'a Pbc2' P2'ca |
| 30 - | c2v.6 | Pnc2 | P2na Pb2n Pn2b Pcn2 P2an |
| 31 - | c2v.7 | Pmn2' | P2'mn Pn2'm Pm2'n Pnm2' P2'nm |
| 32 - | c2v.8 | Pba2 | P2cb Pc2a |
| 33 - | c2v.9 | Pna2 | P2'nb Pc2'n Pn2'a Pbn2' P2'cn |
| 34 - | c2v10 | Pnn2 | P2nn Pn2n |
| 35 - | c2v11 | Cmm2 | A2mm Bm2m |
| 36 - | c2v12 | Cmc2' | A2'ma Bb2'm Bm2'b Ccm2' A2'am |
| 37 - | c2v13 | Ccc2 | A2aa Bb2b |
| 38 - | c2v14 | Amm2 | B2mm Cm2m Am2m Bmm2 C2mm |
| 39 - | c2v15 | Abm2 | B2cm Cm2a Ac2m Bma2 C2mb |
| 40 - | c2v16 | Ama2 | B2mb Cc2m Am2a Bbm2 C2cm |
| 41 - | c2v17 | Aba2 | B2cb Cc2a Ac2a Bba2 C2cb |
| 42 - | c2v18 | Fmm2 | F2mm Fm2m |
| 43 - | c2v19 | Fdd2 | F2dd Fd2d |
| 44 - | c2v20 | Imm2 | I2mm Im2m |
| 45 - | c2v21 | Iba2 | I2cb Ic2a |
| 46 - | c2v22 | Ima2 | I2mb Ic2m Im2a Ibm2 I2cm |
| 47 - | d2h.1 | Pmmm | |
| 48 - | d2h.2 | Pnnn | |
| 49 - | d2h.3 | Pccm | Pmaa Pbmb |
| 50 - | d2h.4 | Pban | Pncb Pcna |
| 51 - | d2h.5 | Pmma | Pbmm Pmcm Pmam Pmmb Pcmm |
| 52 - | d2h.6 | Pnna | Pbnn Pncn Pnan Pnnb Pcnn |
| 53 - | d2h.7 | Pmna | Pbmn Pncm Pman Pnmb Pcnm |
| 54 - | d2h.8 | Pcca | Pbaa Pbcb Pbab Pccb Pcaa |
| 55 - | d2h.9 | Pbam | Pmcb Pcma |
| 56 - | d2h10 | Pccn | Pnaa Pbnb |
| 57 - | d2h11 | Pbcm | Pmca Pbma Pcmb Pcam Pmab |
| 58 - | d2h12 | Pnnm | Pmnn Pnmn |
| 59 - | d2h13 | Pmmn | Pnmm Pmnm |
| 60 - | d2h14 | Pbcn | Pnca Pbna Pcnb Pcan Pnab |
| 61 - | d2h15 | Pbca | Pcab |
| 62 - | d2h16 | Pnma | Pbnm Pmcn Pnam Pmnb Pcmn |
| 63 - | d2h17 | Cmcm | Amma Bbmm Bmmb Ccmm Amam |
| 64 - | d2h18 | Cmca | Abma Bbcm Bmab Ccmb Acam |
| 65 - | d2h19 | Cmmm | Bmmm |
| 66 - | d2h20 | Cccm | Amaa Bbmb |
| 67 - | d2h21 | Cmma | Abmm Bmcm Bmam Cmmb Acmm |
| 68 - | d2h22 | Ccca | Abaa Bbcb Bbab Cccb Acaa |
| 69 - | d2h23 | Fmmm | |
| 70 - | d2h24 | Fddd | |
| 71 - | d2h25 | Immm | |
| 72 - | d2h26 | Ibam | Imcb Icma |
| 73 - | d2h27 | Ibca | Icab |
| 74 - | d2h28 | Imma | Ibmm Imcm Imam Immb Icmm |
| 75 - | c4..1 | P4 | C4 |
| 76 - | c4..2 | P4] | C4] |
| 77 - | c4..3 | P4' | C4' |
| 78 - | c4..4 | P4[ | C4[ |
| 79 - | c4..5 | I4 | F4 |
| 80 - | c4..6 | I4] | F4] |
| 81 - | s4..1 | P4~ | C4~ |
| 82 - | s4..2 | I4~ | F4~ |
| 83 - | c4h.1 | P4/m | C4/m |
| 84 - | c4h.2 | P4'/m | C4'/m |
| 85 - | c4h.3 | P4/n | C4/a |
| 86 - | c4h.4 | P4'/n | C4'/a |
| 87 - | c4h.5 | I4/m | F4/m |
| 88 - | c4h.6 | I4]/a | F4]/d |
| 89 - | d4..1 | P422 | C422 |
| 90 - | d4..2 | P42'2 | C422' |
| 91 - | d4..3 | P4]22 | C4]22 |
| 92 - | d4..4 | P4]2'2 | C4]22' |
| 93 - | d4..5 | P4'22 | C4'22 |
| 94 - | d4..6 | P4'2'2 | C4'22' |
| 95 - | d4..7 | P4[22 | C4[22 |
| 96 - | d4..8 | P4[2'2 | C4[22' |
| 97 - | d4..9 | I422 | F422 |
| 98 - | d4.10 | I4]22 | F4]22 |
| 99 - | c4v.1 | P4mm | C4mm |
| 100 - | c4v.2 | P4bm | C4mb |
| 101 - | c4v.3 | P4'cm | C4'mc |
| 102 - | c4v.4 | P4'nm | C4'mn |
| 103 - | c4v.5 | P4cc | C4cc |
| 104 - | c4v.6 | P4nc | C4cn |
| 105 - | c4v.7 | P4'mc | C4'cm |
| 106 - | c4v.8 | P4'bc | C4'cb |
| 107 - | c4v.9 | I4mm | F4mm |
| 108 - | c4v10 | I4cm | F4mc |
| 109 - | c4v11 | I4]md | F4]dm |
| 110 - | c4v12 | I4]cd | F4]dc |
| 111 - | d2d.1 | P4~2m | C4~m2 |
| 112 - | d2d.2 | P4~2c | C4~c2 |
| 113 - | d2d.3 | P4~2'm | C4~m2' |
| 114 - | d2d.4 | P4~2'c | C4~c2' |
| 115 - | d2d.4 | P4~2'c | C4~c2' |
| 116 - | d2d.5 | P4~m2 | C4~2m |
| 117 - | d2d.6 | P4~c2 | C4~2c |
| 118 - | d2d.7 | P4~b2 | C4~2b |
| 119 - | d2d.8 | P4~n2 | C4~2n |
| 120 - | d2d.9 | I4~m2 | F4~2m |
| 121 - | d2d10 | I4~c2 | F4~2c |
| 122 - | d2d11 | I4~2m | F4~m2 |
| 123 - | d2d12 | I4~2d | F4~d2 |
| 124 - | d4h.1 | P4/mmm | C4/mmm |
| 125 - | d4h.2 | P4/mcc | C4/mcc |
| 126 - | d4h.3 | P4/nbm | C4/amb |
| 127 - | d4h.4 | P4/nnc | C4/acn |
| 128 - | d4h.5 | P4/mbm | C4/mmb |
| 129 - | d4h.6 | P4/mnc | C4/mcn |
| 130 - | d4h.7 | P4/nmm | C4/amm |
| 131 - | d4h.8 | P4/ncc | C4/acc |
| 132 - | d4h.9 | P4'/mmc | C4'/mcm |
| 133 - | d4h10 | P4'/mcm | C4'/mmc |
| 134 - | d4h11 | P4'/nbc | C4'/acb |
| 135 - | d4h12 | P4'/nnm | C4'/amn |
| 136 - | d4h13 | P4'/mbc | C4'/mcb |
| 137 - | d4h14 | P4'/mnm | C4'/mmn |
| 138 - | d4h15 | P4'/nmc | C4'/acm |
| 139 - | d4h16 | P4'/ncm | C4'/amc |
| 140 - | d4h17 | I4/mmm | F4/mmm |
| 141 - | d4h18 | I4/mcm | F4/mmc |
| 142 - | d4h19 | I4]/amd | F4]/ddm |
| 143 - | d4h20 | I4]/acd | F4]/ddc |
| 144 - | c3..1 | P3 | |
| 145 - | c3..2 | P3] | |
| 146 - | c3..3 | P3[ | R3 |
| 147 - | c3i.1 | 1 P3~ | |
| 148 - | c3i.2 | R3~ | |
| 149 - | d3..1 | P312 | |
| 150 - | d3..2 | P321 | |
| 151 - | d3..3 | P3]12 | |
| 152 - | d3..4 | P3]21 | |
| 153 - | d3..5 | P3[12 | |
| 154 - | d3..6 | P3[21 | |
| 155 - | d3..7 | R32 | |
| 156 - | c3v.1 | P3m1 | |
| 157 - | c3v.2 | P31m | |
| 158 - | c3v.3 | P3c1 | |
| 159 - | c3v.4 | P31c | |
| 160 - | c3v.5 | R3m | |
| 161 - | c3v.6 | R3c | |
| 162 - | d3d.1 | P3~1m | |
| 163 - | d3d.2 | P3~1c | |
| 164 - | d3d.3 | P3~m1 | |
| 165 - | d3d.4 | P3~c1 | |
| 166 - | d3d.5 | R3~m | |
| 167 - | d3d.6 | R3~c | |
| 168 - | c6..1 | P6 | |
| 169 - | c6..2 | P6] | |
| 170 - | c6..3 | P6[ | |
| 171 - | c6..4 | P6} | |
| 172 - | c6..5 | P6{ | |
| 173 - | c6..6 | P6' | |
| 174 - | c3h.1 | P6~ | |
| 175 - | c6h.1 | P6/m | |
| 176 - | c6h.2 | P6'/m | |
| 177 - | d6..1 | P622 | |
| 178 - | d6..2 | P6]22 | |
| 179 - | d6..3 | P6[22 | |
| 180 - | d6..4 | P6}22 | |
| 181 - | d6..5 | P6{22 | |
| 182 - | d6..6 | P6'22 | |
| 183 - | c6v.1 | P6mm | |
| 184 - | c6v.2 | P6cc | |
| 185 - | c6v.3 | P6'cm | |
| 186 - | c6v.4 | P6'mc | |
| 187 - | d3h.1 | P6~m2 | |
| 188 - | d3h.2 | P6~c2 | |
| 189 - | d3h.3 | P6~2m | |
| 190 - | d3h.4 | P6~2c | |
| 191 - | d6h.1 | P6/mmm | |
| 192 - | d6h.2 | P6/mcc | |
| 193 - | d6h.3 | P6'/mcm | |
| 194 - | d6h.4 | P6'/mmc | |
| 195 - | t...1 | P23 | |
| 196 - | t...2 | F23 | |
| 197 - | t...3 | I23 | |
| 198 - | t...4 | P2'3 | |
| 199 - | t...5 | I2'3 | |
| 200 - | th..1 | Pm3 | |
| 201 - | th..2 | Pn3 | |
| 202 - | th..3 | Fm3 | |
| 203 - | th..4 | Fd3 | |
| 204 - | th..5 | Im3 | |
| 205 - | th..6 | Pa3 | |
| 206 - | th..7 | Ia3 | |
| 207 - | o...1 | P432 | |
| 208 - | o...2 | P4'32 | |
| 209 - | o...3 | F432 | |
| 210 - | o...4 | F4]32 | |
| 211 - | o...5 | I432 | |
| 212 - | o...6 | P4[32 | |
| 213 - | o...7 | P4]32 | |
| 214 - | o...8 | I4]32 | |
| 215 - | td..1 | P4~3m | |
| 216 - | td..2 | F4~3m | |
| 217 - | td..3 | I4~3m | |
| 218 - | td..4 | P4~3n | |
| 219 - | td..5 | F4~3c | |
| 220 - | td..6 | I4~3d | |
| 221 - | oh..1 | Pm3m | |
| 222 - | oh..2 | Pn3n | |
| 223 - | oh..3 | Pm3n | |
| 224 - | oh..4 | Pn3m | |
| 225 - | oh..5 | Fm3m | |
| 226 - | oh..6 | Fm3c | |
| 227 - | oh..7 | Fd3m | |
| 228 - | oh..8 | Fd3c | |
| 229 - | oh..9 | Im3m | |
| 230 - | oh.10 | Ia3d |
| If you have any comments or suggestions, please let me know. |