Crystallograpic Systems

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Crystallograpic Systems

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Crystallographic Systems

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	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). 6_{1, 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). 4_1,2,3 = 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). 4_1,2,3 = 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)

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