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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.

1. New symbols for the seven crystal systems.

ci*** triclinic
c2h** monoclinic
d2h** orthorhombic
d4h** tetragonal
d3d** trigonal
d6h** hexagonal
oh*** isometric


2. New symbols for the 32 point groups.
Left column - new symbol Schoenflies type
Right column - Hermann-Mauguin type

c1... 1
ci... 1~
c2... 2
cs... m
c2h.. 2/m
d2... 2 2 2
c2v.. m m 2
d2h.. m m m
c4... 4
s4... 4~
c4h.. 4/m
d4... 4 2 2
c4v.. 4 m m
d2d.. 4~2 m
d4h.. 4/m m m
c3... 3
c3i.. 3~
c3v.. 3 m
d3... 3 2
d3d.. 3~m
c6... 6
c3h.. 6~
c6h.. 6/m
d6... 6 2 2
c6v.. 6 m m
d3h.. 6~2 m
d6h.. 6 m m
t.... 2 3
th... m 3
o.... 4 3 2
td... 4~3 m
oh... m 3 m


3. New symbols for the 230 space groups.
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.