See the crystallography section for more details.
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)
Triclinic - Pinacoidal
Monoclinic
Monoclinic - Domatic
(m)
Monoclinic - Sphenoidal
(2)
Monoclinic - Prismatic
(2/m)
Orthorhombic
Orthorhombic - Pyramidal
(mm2)
Orthorhombic - Disphenoidal
(2 2 2)
Orthorhombic - Dipyramidal
(2/m 2/m 2/m)
Trigonal
Trigonal - Pyramidal
(3)
Trigonal - Rhombohedral
Trigonal - Ditrigonal Pyramidal
(3m)
Trigonal - Trapezohedral
(3 2)
Trigonal - Hexagonal Scalenohedral
(3 2/m)
Hexagonal
Hexagonal - Trigonal Dipyramidal
(6)
Hexagonal - Pyramidal
Hexagonal - Dipyramidal
(6/m)
Hexagonal - Ditrigonal Dipyramidal
(6 m2)
Hexagonal - Dihexagonal Pyramidal
(6mm)
Hexagonal - Trapezohedral
(6 2 2)
Hexagonal - Dihexagonal Dipyramidal
(6/m 2/m 2/m)
Tetragonal
Tetragonal - Disphenoidal
(4)
Tetragonal - Pyramidal
Tetragonal - Dipyramidal
(4/m)
Tetragonal - Scalenohedral
(4 2m)
Tetragonal - Ditetragonal Pyramidal
(4mm)
Tetragonal - Trapezohedral
(4 2 2)
Tetragonal - Ditetragonal Dipyramidal
(4/m 2/m 2/m)
Isometric
Isometric - Tetartoidal
(2 3)
Isometric - Diploidal
(2/m 3)
Isometric - Hextetrahedral
(4 3m)
Isometric - Gyroidal
(4 3 2)
Isometric - Hexoctahedral
(4/m 3 2/m)
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)
Example Subject Searches
Example: Isometric Gyroidal finds all minerals that are Isometric Gyroidal.