This figure is a summary of the seven crystal systems in relation to some everyday objects.
A triclinic crystal, such as plagioclase feldspar or kyanite, can be likened to a packet of envelopes pushed askew in two directions. No edges or angles are the same, and it has no axis of symmetry.
A monoclinic crystal, such as gypsum, mica, orthoclase feldspar, hornblende, augite or talc, can be likened to a partially squashed matchbox cover, flattened or skewed to one side. No edges are the same, with alpha and gamma both at 90 degrees, but not beta. It has one two-fold axis of symmetry.
An orthorhombic crystal, such as barite, topaz, olivine or andalusite, can be likened to a matchbox. No edges are the same, but all angles are at 90 degrees. It has three two-fold axes of symmetry at 90 degrees to each other.
A tetragonal crystal, such as chalcopyrite or zircon, can be likened to two sugar cubes stuck together. Edges a and b are the same, but not c, while all angles are at 90 degrees. It has one four-fold axis of symmetry.
A cubic crystal, such as galena, halite, pyrite, fluorite or sphalerite, can be likened to a single sugar cube. All edges are the same, and all angles are at 90 degrees. It has four three-fold axes of symmetry, through the corners of the crystal.
A trigonal crystal, such as calcite, tourmaline or corundum, can be likened to a triangular prism. All edges are the same, with alpha, beta and gamma all the same, but the angles are not. It has one three-fold axis of symmetry.
A hexagonal crystal, such as apatite or beryl, can be likened to a hexagonal prism. Edges a and b are the same, but not b, with both alpha and gamma at 90 degrees but gamma at 120 degrees. It has one six-fold axis of symmetry.