Extensions
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Monoclinic unique axis b unique axis c unique axis a
abc c-ba abc ba-c abc -acb
------------ ------------ ------------
cell choice 1 :b1 :-b1 :c1 :-c1 :a1 :-a1
2 :b2 :-b2 :c2 :-c2 :a2 :-a2
3 :b3 :-b3 :c3 :-c3 :a3 :-a3
Orthorhombic :ba-c change of basis abc -> ba-c
:1 origin choice 1
:2ba-c origin choice 2, change of basis abc -> ba-c
Tetragonal :1 origin choice 1
Cubic :2 origin choice 2
Trigonal :H hexagonal axes
:R rhombohedral axes
Number Schoenflies Hermann-Mauguin Hall
------ ----------- --------------- ----
1 C1^1 P1 P 1
2 Ci^1 P-1 -P 1
3:b C2^1 P2:b = P121 P 2y
3:c C2^1 P2:c = P112 P 2
3:a C2^1 P2:a = P211 P 2x
4:b C2^2 P21:b = P1211 P 2yb
4:c C2^2 P21:c = P1121 P 2c
4:a C2^2 P21:a = P2111 P 2xa
5:b1 C2^3 C2:b1 = C121 C 2y
5:b2 C2^3 C2:b2 = A121 A 2y
5:b3 C2^3 C2:b3 = I121 I 2y
5:c1 C2^3 C2:c1 = A112 A 2
5:c2 C2^3 C2:c2 = B112 = B2 B 2
5:c3 C2^3 C2:c3 = I112 I 2
5:a1 C2^3 C2:a1 = B211 B 2x
5:a2 C2^3 C2:a2 = C211 C 2x
5:a3 C2^3 C2:a3 = I211 I 2x
6:b Cs^1 Pm:b = P1m1 P -2y
6:c Cs^1 Pm:c = P11m P -2
6:a Cs^1 Pm:a = Pm11 P -2x
7:b1 Cs^2 Pc:b1 = P1c1 P -2yc
7:b2 Cs^2 Pc:b2 = P1n1 P -2yac
7:b3 Cs^2 Pc:b3 = P1a1 P -2ya
7:c1 Cs^2 Pc:c1 = P11a P -2a
7:c2 Cs^2 Pc:c2 = P11n P -2ab
7:c3 Cs^2 Pc:c3 = P11b = Pb P -2b
7:a1 Cs^2 Pc:a1 = Pb11 P -2xb
7:a2 Cs^2 Pc:a2 = Pn11 P -2xbc
7:a3 Cs^2 Pc:a3 = Pc11 P -2xc
8:b1 Cs^3 Cm:b1 = C1m1 C -2y
8:b2 Cs^3 Cm:b2 = A1m1 A -2y
8:b3 Cs^3 Cm:b3 = I1m1 I -2y
8:c1 Cs^3 Cm:c1 = A11m A -2
8:c2 Cs^3 Cm:c2 = B11m = Bm B -2
8:c3 Cs^3 Cm:c3 = I11m I -2
8:a1 Cs^3 Cm:a1 = Bm11 B -2x
8:a2 Cs^3 Cm:a2 = Cm11 C -2x
8:a3 Cs^3 Cm:a3 = Im11 I -2x
9:b1 Cs^4 Cc:b1 = C1c1 C -2yc
9:b2 Cs^4 Cc:b2 = A1n1 A -2yac
9:b3 Cs^4 Cc:b3 = I1a1 I -2ya
9:-b1 Cs^4 Cc:-b1 = A1a1 A -2ya
9:-b2 Cs^4 Cc:-b2 = C1n1 C -2ybc
9:-b3 Cs^4 Cc:-b3 = I1c1 I -2yc
9:c1 Cs^4 Cc:c1 = A11a A -2a
9:c2 Cs^4 Cc:c2 = B11n B -2bc
9:c3 Cs^4 Cc:c3 = I11b I -2b
9:-c1 Cs^4 Cc:-c1 = B11b = Bb B -2b
9:-c2 Cs^4 Cc:-c2 = A11n A -2ac
9:-c3 Cs^4 Cc:-c3 = I11a I -2a
9:a1 Cs^4 Cc:a1 = Bb11 B -2xb
9:a2 Cs^4 Cc:a2 = Cn11 C -2xbc
9:a3 Cs^4 Cc:a3 = Ic11 I -2xc
9:-a1 Cs^4 Cc:-a1 = Cc11 C -2xc
9:-a2 Cs^4 Cc:-a2 = Bn11 B -2xbc
9:-a3 Cs^4 Cc:-a3 = Ib11 I -2xb
10:b C2h^1 P2/m:b = P12/m1 -P 2y
10:c C2h^1 P2/m:c = P112/m -P 2
10:a C2h^1 P2/m:a = P2/m11 -P 2x
11:b C2h^2 P21/m:b = P121/m1 -P 2yb
11:c C2h^2 P21/m:c = P1121/m -P 2c
11:a C2h^2 P21/m:a = P21/m11 -P 2xa
12:b1 C2h^3 C2/m:b1 = C12/m1 -C 2y
12:b2 C2h^3 C2/m:b2 = A12/m1 -A 2y
12:b3 C2h^3 C2/m:b3 = I12/m1 -I 2y
12:c1 C2h^3 C2/m:c1 = A112/m -A 2
12:c2 C2h^3 C2/m:c2 = B112/m = B2/m -B 2
12:c3 C2h^3 C2/m:c3 = I112/m -I 2
12:a1 C2h^3 C2/m:a1 = B2/m11 -B 2x
12:a2 C2h^3 C2/m:a2 = C2/m11 -C 2x
12:a3 C2h^3 C2/m:a3 = I2/m11 -I 2x
13:b1 C2h^4 P2/c:b1 = P12/c1 -P 2yc
13:b2 C2h^4 P2/c:b2 = P12/n1 -P 2yac
13:b3 C2h^4 P2/c:b3 = P12/a1 -P 2ya
13:c1 C2h^4 P2/c:c1 = P112/a -P 2a
13:c2 C2h^4 P2/c:c2 = P112/n -P 2ab
13:c3 C2h^4 P2/c:c3 = P112/b = P2/b -P 2b
13:a1 C2h^4 P2/c:a1 = P2/b11 -P 2xb
13:a2 C2h^4 P2/c:a2 = P2/n11 -P 2xbc
13:a3 C2h^4 P2/c:a3 = P2/c11 -P 2xc
14:b1 C2h^5 P21/c:b1 = P121/c1 -P 2ybc
14:b2 C2h^5 P21/c:b2 = P121/n1 -P 2yn
14:b3 C2h^5 P21/c:b3 = P121/a1 -P 2yab
14:c1 C2h^5 P21/c:c1 = P1121/a -P 2ac
14:c2 C2h^5 P21/c:c2 = P1121/n -P 2n
14:c3 C2h^5 P21/c:c3 = P1121/b = P21/b -P 2bc
14:a1 C2h^5 P21/c:a1 = P21/b11 -P 2xab
14:a2 C2h^5 P21/c:a2 = P21/n11 -P 2xn
14:a3 C2h^5 P21/c:a3 = P21/c11 -P 2xac
15:b1 C2h^6 C2/c:b1 = C12/c1 -C 2yc
15:b2 C2h^6 C2/c:b2 = A12/n1 -A 2yac
15:b3 C2h^6 C2/c:b3 = I12/a1 -I 2ya
15:-b1 C2h^6 C2/c:-b1 = A12/a1 -A 2ya
15:-b2 C2h^6 C2/c:-b2 = C12/n1 -C 2ybc
15:-b3 C2h^6 C2/c:-b3 = I12/c1 -I 2yc
15:c1 C2h^6 C2/c:c1 = A112/a -A 2a
15:c2 C2h^6 C2/c:c2 = B112/n -B 2bc
15:c3 C2h^6 C2/c:c3 = I112/b -I 2b
15:-c1 C2h^6 C2/c:-c1 = B112/b = B2/b -B 2b
15:-c2 C2h^6 C2/c:-c2 = A112/n -A 2ac
15:-c3 C2h^6 C2/c:-c3 = I112/a -I 2a
15:a1 C2h^6 C2/c:a1 = B2/b11 -B 2xb
15:a2 C2h^6 C2/c:a2 = C2/n11 -C 2xbc
15:a3 C2h^6 C2/c:a3 = I2/c11 -I 2xc
15:-a1 C2h^6 C2/c:-a1 = C2/c11 -C 2xc
15:-a2 C2h^6 C2/c:-a2 = B2/n11 -B 2xbc
15:-a3 C2h^6 C2/c:-a3 = I2/b11 -I 2xb
16 D2^1 P222 P 2 2
17 D2^2 P2221 P 2c 2
17:cab D2^2 P2122 P 2a 2a
17:bca D2^2 P2212 P 2 2b
18 D2^3 P21212 P 2 2ab
18:cab D2^3 P22121 P 2bc 2
18:bca D2^3 P21221 P 2ac 2ac
19 D2^4 P212121 P 2ac 2ab
20 D2^5 C2221 C 2c 2
20:cab D2^5 A2122 A 2a 2a
20:bca D2^5 B2212 B 2 2b
21 D2^6 C222 C 2 2
21:cab D2^6 A222 A 2 2
21:bca D2^6 B222 B 2 2
22 D2^7 F222 F 2 2
23 D2^8 I222 I 2 2
24 D2^9 I212121 I 2b 2c
25 C2v^1 Pmm2 P 2 -2
25:cab C2v^1 P2mm P -2 2
25:bca C2v^1 Pm2m P -2 -2
26 C2v^2 Pmc21 P 2c -2
26:ba-c C2v^2 Pcm21 P 2c -2c
26:cab C2v^2 P21ma P -2a 2a
26:-cba C2v^2 P21am P -2 2a
26:bca C2v^2 Pb21m P -2 -2b
26:a-cb C2v^2 Pm21b P -2b -2
27 C2v^3 Pcc2 P 2 -2c
27:cab C2v^3 P2aa P -2a 2
27:bca C2v^3 Pb2b P -2b -2b
28 C2v^4 Pma2 P 2 -2a
28:ba-c C2v^4 Pbm2 P 2 -2b
28:cab C2v^4 P2mb P -2b 2
28:-cba C2v^4 P2cm P -2c 2
28:bca C2v^4 Pc2m P -2c -2c
28:a-cb C2v^4 Pm2a P -2a -2a
29 C2v^5 Pca21 P 2c -2ac
29:ba-c C2v^5 Pbc21 P 2c -2b
29:cab C2v^5 P21ab P -2b 2a
29:-cba C2v^5 P21ca P -2ac 2a
29:bca C2v^5 Pc21b P -2bc -2c
29:a-cb C2v^5 Pb21a P -2a -2ab
30 C2v^6 Pnc2 P 2 -2bc
30:ba-c C2v^6 Pcn2 P 2 -2ac
30:cab C2v^6 P2na P -2ac 2
30:-cba C2v^6 P2an P -2ab 2
30:bca C2v^6 Pb2n P -2ab -2ab
30:a-cb C2v^6 Pn2b P -2bc -2bc
31 C2v^7 Pmn21 P 2ac -2
31:ba-c C2v^7 Pnm21 P 2bc -2bc
31:cab C2v^7 P21mn P -2ab 2ab
31:-cba C2v^7 P21nm P -2 2ac
31:bca C2v^7 Pn21m P -2 -2bc
31:a-cb C2v^7 Pm21n P -2ab -2
32 C2v^8 Pba2 P 2 -2ab
32:cab C2v^8 P2cb P -2bc 2
32:bca C2v^8 Pc2a P -2ac -2ac
33 C2v^9 Pna21 P 2c -2n
33:ba-c C2v^9 Pbn21 P 2c -2ab
33:cab C2v^9 P21nb P -2bc 2a
33:-cba C2v^9 P21cn P -2n 2a
33:bca C2v^9 Pc21n P -2n -2ac
33:a-cb C2v^9 Pn21a P -2ac -2n
34 C2v^10 Pnn2 P 2 -2n
34:cab C2v^10 P2nn P -2n 2
34:bca C2v^10 Pn2n P -2n -2n
35 C2v^11 Cmm2 C 2 -2
35:cab C2v^11 A2mm A -2 2
35:bca C2v^11 Bm2m B -2 -2
36 C2v^12 Cmc21 C 2c -2
36:ba-c C2v^12 Ccm21 C 2c -2c
36:cab C2v^12 A21ma A -2a 2a
36:-cba C2v^12 A21am A -2 2a
36:bca C2v^12 Bb21m B -2 -2b
36:a-cb C2v^12 Bm21b B -2b -2
37 C2v^13 Ccc2 C 2 -2c
37:cab C2v^13 A2aa A -2a 2
37:bca C2v^13 Bb2b B -2b -2b
38 C2v^14 Amm2 A 2 -2
38:ba-c C2v^14 Bmm2 B 2 -2
38:cab C2v^14 B2mm B -2 2
38:-cba C2v^14 C2mm C -2 2
38:bca C2v^14 Cm2m C -2 -2
38:a-cb C2v^14 Am2m A -2 -2
39 C2v^15 Abm2 A 2 -2c
39:ba-c C2v^15 Bma2 B 2 -2c
39:cab C2v^15 B2cm B -2c 2
39:-cba C2v^15 C2mb C -2b 2
39:bca C2v^15 Cm2a C -2b -2b
39:a-cb C2v^15 Ac2m A -2c -2c
40 C2v^16 Ama2 A 2 -2a
40:ba-c C2v^16 Bbm2 B 2 -2b
40:cab C2v^16 B2mb B -2b 2
40:-cba C2v^16 C2cm C -2c 2
40:bca C2v^16 Cc2m C -2c -2c
40:a-cb C2v^16 Am2a A -2a -2a
41 C2v^17 Aba2 A 2 -2ac
41:ba-c C2v^17 Bba2 B 2 -2bc
41:cab C2v^17 B2cb B -2bc 2
41:-cba C2v^17 C2cb C -2bc 2
41:bca C2v^17 Cc2a C -2bc -2bc
41:a-cb C2v^17 Ac2a A -2ac -2ac
42 C2v^18 Fmm2 F 2 -2
42:cab C2v^18 F2mm F -2 2
42:bca C2v^18 Fm2m F -2 -2
43 C2v^19 Fdd2 F 2 -2d
43:cab C2v^19 F2dd F -2d 2
43:bca C2v^19 Fd2d F -2d -2d
44 C2v^20 Imm2 I 2 -2
44:cab C2v^20 I2mm I -2 2
44:bca C2v^20 Im2m I -2 -2
45 C2v^21 Iba2 I 2 -2c
45:cab C2v^21 I2cb I -2a 2
45:bca C2v^21 Ic2a I -2b -2b
46 C2v^22 Ima2 I 2 -2a
46:ba-c C2v^22 Ibm2 I 2 -2b
46:cab C2v^22 I2mb I -2b 2
46:-cba C2v^22 I2cm I -2c 2
46:bca C2v^22 Ic2m I -2c -2c
46:a-cb C2v^22 Im2a I -2a -2a
47 D2h^1 Pmmm -P 2 2
48:1 D2h^2 Pnnn:1 P 2 2 -1n
48:2 D2h^2 Pnnn:2 -P 2ab 2bc
49 D2h^3 Pccm -P 2 2c
49:cab D2h^3 Pmaa -P 2a 2
49:bca D2h^3 Pbmb -P 2b 2b
50:1 D2h^4 Pban:1 P 2 2 -1ab
50:2 D2h^4 Pban:2 -P 2ab 2b
50:1cab D2h^4 Pncb:1 P 2 2 -1bc
50:2cab D2h^4 Pncb:2 -P 2b 2bc
50:1bca D2h^4 Pcna:1 P 2 2 -1ac
50:2bca D2h^4 Pcna:2 -P 2a 2c
51 D2h^5 Pmma -P 2a 2a
51:ba-c D2h^5 Pmmb -P 2b 2
51:cab D2h^5 Pbmm -P 2 2b
51:-cba D2h^5 Pcmm -P 2c 2c
51:bca D2h^5 Pmcm -P 2c 2
51:a-cb D2h^5 Pmam -P 2 2a
52 D2h^6 Pnna -P 2a 2bc
52:ba-c D2h^6 Pnnb -P 2b 2n
52:cab D2h^6 Pbnn -P 2n 2b
52:-cba D2h^6 Pcnn -P 2ab 2c
52:bca D2h^6 Pncn -P 2ab 2n
52:a-cb D2h^6 Pnan -P 2n 2bc
53 D2h^7 Pmna -P 2ac 2
53:ba-c D2h^7 Pnmb -P 2bc 2bc
53:cab D2h^7 Pbmn -P 2ab 2ab
53:-cba D2h^7 Pcnm -P 2 2ac
53:bca D2h^7 Pncm -P 2 2bc
53:a-cb D2h^7 Pman -P 2ab 2
54 D2h^8 Pcca -P 2a 2ac
54:ba-c D2h^8 Pccb -P 2b 2c
54:cab D2h^8 Pbaa -P 2a 2b
54:-cba D2h^8 Pcaa -P 2ac 2c
54:bca D2h^8 Pbcb -P 2bc 2b
54:a-cb D2h^8 Pbab -P 2b 2ab
55 D2h^9 Pbam -P 2 2ab
55:cab D2h^9 Pmcb -P 2bc 2
55:bca D2h^9 Pcma -P 2ac 2ac
56 D2h^10 Pccn -P 2ab 2ac
56:cab D2h^10 Pnaa -P 2ac 2bc
56:bca D2h^10 Pbnb -P 2bc 2ab
57 D2h^11 Pbcm -P 2c 2b
57:ba-c D2h^11 Pcam -P 2c 2ac
57:cab D2h^11 Pmca -P 2ac 2a
57:-cba D2h^11 Pmab -P 2b 2a
57:bca D2h^11 Pbma -P 2a 2ab
57:a-cb D2h^11 Pcmb -P 2bc 2c
58 D2h^12 Pnnm -P 2 2n
58:cab D2h^12 Pmnn -P 2n 2
58:bca D2h^12 Pnmn -P 2n 2n
59:1 D2h^13 Pmmn:1 P 2 2ab -1ab
59:2 D2h^13 Pmmn:2 -P 2ab 2a
59:1cab D2h^13 Pnmm:1 P 2bc 2 -1bc
59:2cab D2h^13 Pnmm:2 -P 2c 2bc
59:1bca D2h^13 Pmnm:1 P 2ac 2ac -1ac
59:2bca D2h^13 Pmnm:2 -P 2c 2a
60 D2h^14 Pbcn -P 2n 2ab
60:ba-c D2h^14 Pcan -P 2n 2c
60:cab D2h^14 Pnca -P 2a 2n
60:-cba D2h^14 Pnab -P 2bc 2n
60:bca D2h^14 Pbna -P 2ac 2b
60:a-cb D2h^14 Pcnb -P 2b 2ac
61 D2h^15 Pbca -P 2ac 2ab
61:ba-c D2h^15 Pcab -P 2bc 2ac
62 D2h^16 Pnma -P 2ac 2n
62:ba-c D2h^16 Pmnb -P 2bc 2a
62:cab D2h^16 Pbnm -P 2c 2ab
62:-cba D2h^16 Pcmn -P 2n 2ac
62:bca D2h^16 Pmcn -P 2n 2a
62:a-cb D2h^16 Pnam -P 2c 2n
63 D2h^17 Cmcm -C 2c 2
63:ba-c D2h^17 Ccmm -C 2c 2c
63:cab D2h^17 Amma -A 2a 2a
63:-cba D2h^17 Amam -A 2 2a
63:bca D2h^17 Bbmm -B 2 2b
63:a-cb D2h^17 Bmmb -B 2b 2
64 D2h^18 Cmca -C 2bc 2
64:ba-c D2h^18 Ccmb -C 2bc 2bc
64:cab D2h^18 Abma -A 2ac 2ac
64:-cba D2h^18 Acam -A 2 2ac
64:bca D2h^18 Bbcm -B 2 2bc
64:a-cb D2h^18 Bmab -B 2bc 2
65 D2h^19 Cmmm -C 2 2
65:cab D2h^19 Ammm -A 2 2
65:bca D2h^19 Bmmm -B 2 2
66 D2h^20 Cccm -C 2 2c
66:cab D2h^20 Amaa -A 2a 2
66:bca D2h^20 Bbmb -B 2b 2b
67 D2h^21 Cmma -C 2b 2
67:ba-c D2h^21 Cmmb -C 2b 2b
67:cab D2h^21 Abmm -A 2c 2c
67:-cba D2h^21 Acmm -A 2 2c
67:bca D2h^21 Bmcm -B 2 2c
67:a-cb D2h^21 Bmam -B 2c 2
68:1 D2h^22 Ccca:1 C 2 2 -1bc
68:2 D2h^22 Ccca:2 -C 2b 2bc
68:1ba-c D2h^22 Cccb:1 C 2 2 -1bc
68:2ba-c D2h^22 Cccb:2 -C 2b 2c
68:1cab D2h^22 Abaa:1 A 2 2 -1ac
68:2cab D2h^22 Abaa:2 -A 2a 2c
68:1-cba D2h^22 Acaa:1 A 2 2 -1ac
68:2-cba D2h^22 Acaa:2 -A 2ac 2c
68:1bca D2h^22 Bbcb:1 B 2 2 -1bc
68:2bca D2h^22 Bbcb:2 -B 2bc 2b
68:1a-cb D2h^22 Bbab:1 B 2 2 -1bc
68:2a-cb D2h^22 Bbab:2 -B 2b 2bc
69 D2h^23 Fmmm -F 2 2
70:1 D2h^24 Fddd:1 F 2 2 -1d
70:2 D2h^24 Fddd:2 -F 2uv 2vw
71 D2h^25 Immm -I 2 2
72 D2h^26 Ibam -I 2 2c
72:cab D2h^26 Imcb -I 2a 2
72:bca D2h^26 Icma -I 2b 2b
73 D2h^27 Ibca -I 2b 2c
73:ba-c D2h^27 Icab -I 2a 2b
74 D2h^28 Imma -I 2b 2
74:ba-c D2h^28 Immb -I 2a 2a
74:cab D2h^28 Ibmm -I 2c 2c
74:-cba D2h^28 Icmm -I 2 2b
74:bca D2h^28 Imcm -I 2 2a
74:a-cb D2h^28 Imam -I 2c 2
75 C4^1 P4 P 4
76 C4^2 P41 P 4w
77 C4^3 P42 P 4c
78 C4^4 P43 P 4cw
79 C4^5 I4 I 4
80 C4^6 I41 I 4bw
81 S4^1 P-4 P -4
82 S4^2 I-4 I -4
83 C4h^1 P4/m -P 4
84 C4h^2 P42/m -P 4c
85:1 C4h^3 P4/n:1 P 4ab -1ab
85:2 C4h^3 P4/n:2 -P 4a
86:1 C4h^4 P42/n:1 P 4n -1n
86:2 C4h^4 P42/n:2 -P 4bc
87 C4h^5 I4/m -I 4
88:1 C4h^6 I41/a:1 I 4bw -1bw
88:2 C4h^6 I41/a:2 -I 4ad
89 D4^1 P422 P 4 2
90 D4^2 P4212 P 4ab 2ab
91 D4^3 P4122 P 4w 2c
92 D4^4 P41212 P 4abw 2nw
93 D4^5 P4222 P 4c 2
94 D4^6 P42212 P 4n 2n
95 D4^7 P4322 P 4cw 2c
96 D4^8 P43212 P 4nw 2abw
97 D4^9 I422 I 4 2
98 D4^10 I4122 I 4bw 2bw
99 C4v^1 P4mm P 4 -2
100 C4v^2 P4bm P 4 -2ab
101 C4v^3 P42cm P 4c -2c
102 C4v^4 P42nm P 4n -2n
103 C4v^5 P4cc P 4 -2c
104 C4v^6 P4nc P 4 -2n
105 C4v^7 P42mc P 4c -2
106 C4v^8 P42bc P 4c -2ab
107 C4v^9 I4mm I 4 -2
108 C4v^10 I4cm I 4 -2c
109 C4v^11 I41md I 4bw -2
110 C4v^12 I41cd I 4bw -2c
111 D2d^1 P-42m P -4 2
112 D2d^2 P-42c P -4 2c
113 D2d^3 P-421m P -4 2ab
114 D2d^4 P-421c P -4 2n
115 D2d^5 P-4m2 P -4 -2
116 D2d^6 P-4c2 P -4 -2c
117 D2d^7 P-4b2 P -4 -2ab
118 D2d^8 P-4n2 P -4 -2n
119 D2d^9 I-4m2 I -4 -2
120 D2d^10 I-4c2 I -4 -2c
121 D2d^11 I-42m I -4 2
122 D2d^12 I-42d I -4 2bw
123 D4h^1 P4/mmm -P 4 2
124 D4h^2 P4/mcc -P 4 2c
125:1 D4h^3 P4/nbm:1 P 4 2 -1ab
125:2 D4h^3 P4/nbm:2 -P 4a 2b
126:1 D4h^4 P4/nnc:1 P 4 2 -1n
126:2 D4h^4 P4/nnc:2 -P 4a 2bc
127 D4h^5 P4/mbm -P 4 2ab
128 D4h^6 P4/mnc -P 4 2n
129:1 D4h^7 P4/nmm:1 P 4ab 2ab -1ab
129:2 D4h^7 P4/nmm:2 -P 4a 2a
130:1 D4h^8 P4/ncc:1 P 4ab 2n -1ab
130:2 D4h^8 P4/ncc:2 -P 4a 2ac
131 D4h^9 P42/mmc -P 4c 2
132 D4h^10 P42/mcm -P 4c 2c
133:1 D4h^11 P42/nbc:1 P 4n 2c -1n
133:2 D4h^11 P42/nbc:2 -P 4ac 2b
134:1 D4h^12 P42/nnm:1 P 4n 2 -1n
134:2 D4h^12 P42/nnm:2 -P 4ac 2bc
135 D4h^13 P42/mbc -P 4c 2ab
136 D4h^14 P42/mnm -P 4n 2n
137:1 D4h^15 P42/nmc:1 P 4n 2n -1n
137:2 D4h^15 P42/nmc:2 -P 4ac 2a
138:1 D4h^16 P42/ncm:1 P 4n 2ab -1n
138:2 D4h^16 P42/ncm:2 -P 4ac 2ac
139 D4h^17 I4/mmm -I 4 2
140 D4h^18 I4/mcm -I 4 2c
141:1 D4h^19 I41/amd:1 I 4bw 2bw -1bw
141:2 D4h^19 I41/amd:2 -I 4bd 2
142:1 D4h^20 I41/acd:1 I 4bw 2aw -1bw
142:2 D4h^20 I41/acd:2 -I 4bd 2c
143 C3^1 P3 P 3
144 C3^2 P31 P 31
145 C3^3 P32 P 32
146:H C3^4 R3:H R 3
146:R C3^4 R3:R P 3*
147 C3i^1 P-3 -P 3
148:H C3i^2 R-3:H -R 3
148:R C3i^2 R-3:R -P 3*
149 D3^1 P312 P 3 2
150 D3^2 P321 P 3 2"
151 D3^3 P3112 P 31 2c (0 0 1)
152 D3^4 P3121 P 31 2"
153 D3^5 P3212 P 32 2c (0 0 -1)
154 D3^6 P3221 P 32 2"
155:H D3^7 R32:H R 3 2"
155:R D3^7 R32:R P 3* 2
156 C3v^1 P3m1 P 3 -2"
157 C3v^2 P31m P 3 -2
158 C3v^3 P3c1 P 3 -2"c
159 C3v^4 P31c P 3 -2c
160:H C3v^5 R3m:H R 3 -2"
160:R C3v^5 R3m:R P 3* -2
161:H C3v^6 R3c:H R 3 -2"c
161:R C3v^6 R3c:R P 3* -2n
162 D3d^1 P-31m -P 3 2
163 D3d^2 P-31c -P 3 2c
164 D3d^3 P-3m1 -P 3 2"
165 D3d^4 P-3c1 -P 3 2"c
166:H D3d^5 R-3m:H -R 3 2"
166:R D3d^5 R-3m:R -P 3* 2
167:H D3d^6 R-3c:H -R 3 2"c
167:R D3d^6 R-3c:R -P 3* 2n
168 C6^1 P6 P 6
169 C6^2 P61 P 61
170 C6^3 P65 P 65
171 C6^4 P62 P 62
172 C6^5 P64 P 64
173 C6^6 P63 P 6c
174 C3h^1 P-6 P -6
175 C6h^1 P6/m -P 6
176 C6h^2 P63/m -P 6c
177 D6^1 P622 P 6 2
178 D6^2 P6122 P 61 2 (0 0 -1)
179 D6^3 P6522 P 65 2 (0 0 1)
180 D6^4 P6222 P 62 2c (0 0 1)
181 D6^5 P6422 P 64 2c (0 0 -1)
182 D6^6 P6322 P 6c 2c
183 C6v^1 P6mm P 6 -2
184 C6v^2 P6cc P 6 -2c
185 C6v^3 P63cm P 6c -2
186 C6v^4 P63mc P 6c -2c
187 D3h^1 P-6m2 P -6 2
188 D3h^2 P-6c2 P -6c 2
189 D3h^3 P-62m P -6 -2
190 D3h^4 P-62c P -6c -2c
191 D6h^1 P6/mmm -P 6 2
192 D6h^2 P6/mcc -P 6 2c
193 D6h^3 P63/mcm -P 6c 2
194 D6h^4 P63/mmc -P 6c 2c
195 T^1 P23 P 2 2 3
196 T^2 F23 F 2 2 3
197 T^3 I23 I 2 2 3
198 T^4 P213 P 2ac 2ab 3
199 T^5 I213 I 2b 2c 3
200 Th^1 Pm-3 -P 2 2 3
201:1 Th^2 Pn-3:1 P 2 2 3 -1n
201:2 Th^2 Pn-3:2 -P 2ab 2bc 3
202 Th^3 Fm-3 -F 2 2 3
203:1 Th^4 Fd-3:1 F 2 2 3 -1d
203:2 Th^4 Fd-3:2 -F 2uv 2vw 3
204 Th^5 Im-3 -I 2 2 3
205 Th^6 Pa-3 -P 2ac 2ab 3
206 Th^7 Ia-3 -I 2b 2c 3
207 O^1 P432 P 4 2 3
208 O^2 P4232 P 4n 2 3
209 O^3 F432 F 4 2 3
210 O^4 F4132 F 4d 2 3
211 O^5 I432 I 4 2 3
212 O^6 P4332 P 4acd 2ab 3
213 O^7 P4132 P 4bd 2ab 3
214 O^8 I4132 I 4bd 2c 3
215 Td^1 P-43m P -4 2 3
216 Td^2 F-43m F -4 2 3
217 Td^3 I-43m I -4 2 3
218 Td^4 P-43n P -4n 2 3
219 Td^5 F-43c F -4c 2 3
220 Td^6 I-43d I -4bd 2c 3
221 Oh^1 Pm-3m -P 4 2 3
222:1 Oh^2 Pn-3n:1 P 4 2 3 -1n
222:2 Oh^2 Pn-3n:2 -P 4a 2bc 3
223 Oh^3 Pm-3n -P 4n 2 3
224:1 Oh^4 Pn-3m:1 P 4n 2 3 -1n
224:2 Oh^4 Pn-3m:2 -P 4bc 2bc 3
225 Oh^5 Fm-3m -F 4 2 3
226 Oh^6 Fm-3c -F 4c 2 3
227:1 Oh^7 Fd-3m:1 F 4d 2 3 -1d
227:2 Oh^7 Fd-3m:2 -F 4vw 2vw 3
228:1 Oh^8 Fd-3c:1 F 4d 2 3 -1cd
228:2 Oh^8 Fd-3c:2 -F 4cvw 2vw 3
229 Oh^9 Im-3m -I 4 2 3
230 Oh^10 Ia-3d -I 4bd 2c 3