See the crystallography section for more details.
System |
Class Name |
Hermann-Maguin |
Hermann-Maguin Symbols |
Decoding Space Groups |
Triclinic |
(1) |
P1 |
P = Primitive Lattice. 1 = Symmetry Axis (360/1). 1 = Rotoinversion Axis. |
|
(1) |
P1 | |||
Monoclinic |
(m) |
Cc, Cm, Pc, and Pm |
P = Primitive Lattice. C = 1 Face Centered Lattice. 2 = Symmetry Axis (360/2). 2/ = Mirror Plane perpendicular to Axis. 21 = screw symmetric lattice. |
|
(2) |
C2, P2, and P21 | |||
(2/m) |
C2/c, C2/m, P2/c, P2/m, P21/c, and P21/m | |||
Orthorhombic |
(mm2) |
Aba2, Abm2, Ama2, Amm2, Ccc2, Cmc21, Cmm2, Fdd2, Fmm2, Iba2, Ima2, Imm2, Pba2, Pca21, Pcc2, Pma2, Pmc21, Pmm2, Pmn21, Pna21, Pnc2, and Pnn2 |
P = Primitive Lattice. C = 1 Face Centered Lattice. F = 3 Face Centered Lattice. I = Body Centered Lattice. 21 = Screw Axis. 2 = Symmetry Axis (360/2). a,b,c = Perpendicular Glide Planes. m,n = Oblique Glide Planes. |
|
(2 2 2) |
C222, C2221, F222, I212121, I222, P21212, P212121, P222, and P2221 | |||
(2/m 2/m 2/m) |
Ccca, Cccm, Cmca, Cmcm, Cmma, Cmmm, Fddd, Fmmm, Ibam, Ibca, Imma, Immm, Pbam, Pban, Pbca, Pbcm, Pbcn, Pcca, Pccm, Pccn, Pmma, Pmmm, Pmmn, Pmna, Pnma, Pnna, Pnnm, and Pnnn | |||
Trigonal |
(3) |
P3, P31, P32, and R3 |
P = Primitive Lattice. R = Rhombohedral Lattice. 3 = Rotoinversion Axis. 3, 2, 1 = Symmetry Axis (360/n). c= Perpendicular Glide Planes. m = Oblique Glide Planes. |
|
(3) |
P3 and R3 | |||
(3m) |
P31c, P31m, P3c1, P3m1, R3c, and R3m | |||
(3 2) |
P3112, P312, P3121, P321, P3212, P3221, and R32 | |||
(3 2/m) |
P31c, P31m, P3c1, P3m1, R3c, and R3m | |||
Hexagonal |
(6) |
P6 |
P = Primitive Lattice. 6 = Rotoinversion Axis. 6,2 = Symmetry Axis (360/n). 61, 2, 3, 4, 5 = Screw Axis. c = Perpendicular Glide Planes. m = Oblique Glide Planes. |
|
(6) |
P6, P61, P62, P63, P64, and P65 | |||
(6/m) |
P6/m, P6/m, and P63/m | |||
(6 m2) |
P62c, P62c, P62m, P6c2, and P6m2 | |||
(6mm) |
P63cm, P63mc, P6cc, and P6mm | |||
(6 2 2) |
P622, P6122, P6222, P6322, P6422, P6522 | |||
(6/m 2/m 2/m) |
P6/mcc, P6/mmm, P63/mcm, and P63/mmc | |||
Tetragonal |
(4) |
I4 and P4 |
P = Primitive Lattice. I = Body Centered Lattice. 4 = Rotoinversion Axis. 4,2 = Symmetry Axis (360/n). 41,2,3 = Screw Axis. a,b,c = Perpendicular Glide Planes. m,n = Oblique Glide Planes. |
|
(4) |
I4, I41, P4, P41, P42, and P43 | |||
(4/m) |
I4/m, I41/a, P4/m, P4/n, P42/m, and P42/n | |||
(4 2m) |
I42d, I42m, I4c2, I4m2, P421c, P421m, P42c, P42m, P4b2, P4c2, P4m2, and P4n2 | |||
(4mm) |
I4/mcm, I4/mmm, I41/acd, I41/amd, P4/mbm, P4/mcc, P4/mmm, P4/mnc, P4/nbm, P4/ncc, P4/nmm, P4/nnc, P42/mbc, P42/mcm, P42/mmc, P42/mnm, P42/nbc, P42/ncm, P42/nmc, and P42/nnm | |||
(4 2 2) |
I4122, I422, P41212, P4122, P4212, P422, P42212, P4222, P43212, and P4322 | |||
(4/m 2/m 2/m) |
I41cd, I41md, I4cm, I4mm, P42bc, P42cm, P42mc, P42nm, P4bm, P4cc, P4mm, and P4nc | |||
Isometric |
(2 3) |
F23, I213, I23, P213, and P23 |
P = Primitive Lattice. F = 3 Face Centered Lattice. I = Body Centered Lattice. 4 = Rotoinversion Axis. 4,3,2 = Symmetry Axis (360/n). 41,2,3 = Screw Axis. |
|
(2/m 3) |
Fd3, Fm3, Ia3, Im3, Pa3, Pm3, and Pn3 | |||
(4 3m) |
F43c, F43m, I43d, I43m, P43m, and P43n | |||
(4 3 2) |
F432, F4132, I432, I4132, P432, P4132, P4232, and P4332 | |||
(4/m 3 2/m) |
F432, F4132, I432, I4132, P432, P4132, P4232, and P4332 |
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