Definitions
See the crystallography section for more
details.
Morphological Crystallography, Bravais Lattice, and Space Groups
|
System |
Class Name |
Hermann-Maguin
Symbol
(Point Group) |
Hermann-Maguin Symbols
Space Groups in Point Group |
Decoding Space Groups
Bravais Lattice |
Triclinic
 |
Triclinic - Pedial |
(1) |
P1 |
P = Primitive Lattice.
1 = Symmetry Axis (360/1).
1 = Rotoinversion Axis. |
|
Triclinic - Pinacoidal |
(1) |
P1 |
|
Monoclinic
 |
Monoclinic - Domatic |
(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. |
|
Monoclinic - Sphenoidal |
(2) |
C2, P2, and P21 |
|
Monoclinic - Prismatic |
(2/m) |
C2/c, C2/m, P2/c, P2/m, P21/c, and P21/m |
|
Orthorhombic
 |
Orthorhombic - Pyramidal |
(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.
|
|
Orthorhombic - Disphenoidal |
(2 2 2) |
C222, C2221, F222, I212121,
I222, P21212, P212121,
P222, and P2221 |
|
Orthorhombic - Dipyramidal |
(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
 |
Trigonal - Pyramidal |
(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.
|
|
Trigonal
- Rhombohedral |
(3) |
P3 and R3 |
|
Trigonal - Ditrigonal Pyramidal |
(3m) |
P31c, P31m, P3c1, P3m1, R3c, and R3m |
|
Trigonal - Trapezohedral |
(3 2) |
P3112, P312, P3121, P321, P3212,
P3221, and R32 |
|
Trigonal - Hexagonal Scalenohedral |
(3 2/m) |
P31c, P31m, P3c1,
P3m1, R3c, and R3m |
|
Hexagonal
|
Hexagonal - Trigonal Dipyramidal |
(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.
|
|
Hexagonal - Pyramidal |
(6) |
P6, P61, P62, P63, P64,
and P65 |
|
Hexagonal - Dipyramidal |
(6/m) |
P6/m, P6/m, and P63/m |
|
Hexagonal - Ditrigonal Dipyramidal |
(6 m2) |
P62c, P62c, P62m,
P6c2, and P6m2 |
|
Hexagonal - Dihexagonal Pyramidal |
(6mm) |
P63cm, P63mc, P6cc, and P6mm |
|
Hexagonal - Trapezohedral |
(6 2 2) |
P622, P6122, P6222, P6322,
P6422, P6522 |
|
Hexagonal - Dihexagonal Dipyramidal |
(6/m 2/m 2/m) |
P6/mcc, P6/mmm, P63/mcm, and P63/mmc |
|
Tetragonal
 |
Tetragonal - Disphenoidal |
(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.
|
|
Tetragonal - Pyramidal |
(4) |
I4, I41, P4, P41, P42, and
P43 |
|
Tetragonal - Dipyramidal |
(4/m) |
I4/m, I41/a, P4/m, P4/n, P42/m, and
P42/n |
|
Tetragonal - Scalenohedral |
(4 2m) |
I42d, I42m, I4c2,
I4m2, P421c, P421m,
P42c, P42m, P4b2,
P4c2, P4m2, and P4n2 |
|
Tetragonal - Ditetragonal Pyramidal |
(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 |
|
Tetragonal - Trapezohedral |
(4 2 2) |
I4122, I422, P41212, P4122,
P4212, P422, P42212, P4222, P43212,
and P4322 |
|
Tetragonal - Ditetragonal Dipyramidal |
(4/m 2/m 2/m) |
I41cd, I41md, I4cm, I4mm, P42bc,
P42cm, P42mc, P42nm, P4bm, P4cc, P4mm,
and P4nc |
|
Isometric
 |
Isometric - Tetartoidal |
(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.
|
|
Isometric - Diploidal |
(2/m 3) |
Fd3, Fm3, Ia3, Im3, Pa3, Pm3, and Pn3 |
|
Isometric - Hextetrahedral |
(4 3m) |
F43c, F43m, I43d,
I43m, P43m, and P43n |
|
Isometric - Gyroidal |
(4 3 2) |
F432, F4132, I432, I4132, P432, P4132,
P4232, and P4332 |
|
Isometric - Hexoctahedral |
(4/m 3 2/m) |
F432, F4132, I432, I4132, P432, P4132,
P4232, and P4332 |
Other References on Crystallographic Systems
International Union of Crystallography (IUCr)
Macromolecular Crystallography Web Site
(by Bernhard Rupp)
Crystallography 101
Introduction to
Crystallography and Mineral Crystal Systems by Mike and Darcy Howard
U.S. Naval Research Laboratory (Crystal
Structures)
Search the Mineralogy Database
Example Subject Searches
Example: Isometric Gyroidal finds all minerals that are
Isometric Gyroidal.
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