Crystallograpic Systems (original) (raw)

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.

Search the Web