Point groups

Monoclinic point groups I Symmetry element: two-fold axis parallel to b Characteristic forms: Pedions, sphenoids b stereographic projection c b a monoclinic sphenoid

Monoclinic point groups II Point group: m Symmetry element: mirror perpendicular to b Characteristic forms: Pedions, pinacoidsdomes b stereographic projection c b a monoclinic dome

Monoclinic point groups III Example point group: 2/m Symmetry element: two-fold axis parallel to b, mirror perpendicular to b, inversion center. Characteristic forms: Pinacoids, prisms b stereographic projection c b a monoclinic prism

Monoclinic minerals Transparent, bluish crystal aggregate of vivianite on matrix. Santa Eulalia, Chihuahua, Mexico. Several twinned (two crystals “glued” together in an oriented fashion) green crystals of titanite (sphene) on matrix. Capelinha, Minas Gerais, Brazil. 5.5x5x3.5 cm. Faces of the monoclinic prism http://webmineral.com

Tetragonal point groups I Example point group:422 Symmetry element: four-fold axis parallel to the c axis and 2 sets of 2 two-fold axis perpendicular to it. Characteristic forms: trapezohedron Other forms: pinacoid, tetragonal prism ditetragonal prisms, tetragonal dipyramid, and ditetragonal dipyramids h k l a2 a2 a1 a1 tetragonal trapezohedron

Tetragonal point groups II Example point group: 4/m2/m2/m Symmetry element: four-fold axis parallel to the c axis, 2 sets of mirrors parallel to it, a mirror and 2 sets of two-fold axes perpendicular to it. Characteristic forms: ditetragonal dipyramid Other forms: pinacoid, tetragonal prisms ditetragonal prism, tetragonal dipyramids c a2 a1 a1 a2 ditetragonal dipyramid

Tetragonal crystals Narsarsukite Na2(Ti,Fe)Si2 (O,F)11 Mont Saint-Hilaire, Quebec, Canada. Point group: 4/m2/m2/m Mackayite FeTe2 O5(OH) McGuinnity shaft, Goldfield, Esmeralda County, Nevada, USA. Point group: 4/m2/m2/m Schematic projection of the narsarsukite crystal http://webmineral.com

Tetragonal crystals Zircon ZrSiO4 Finnmark, Norway. Crystal diameter 6 cm. Point group 4/m2/m2/m. The crystal shape is composed of a dipyramid and a prism. Scheelite CaWO4 Traversella, Piemont, Italy. Crystal diameter 4.5 cm. Point group 4/m. The crystal shape is composed of a dipyramid and if only the macroscopic shape is taken the resulting point group would be the same as for zircon. The lowering of the point group is due to the microscopic symmetry. http://webmineral.brgm.fr:8003

Triclinic, monoclinic and orthorhombic forms Dihedrons Pedion Pinacoid Dome Sphenoid Orthorhombic prism Orthorhombic pyramid Orthorhombic dipyramid Orthorhombic disphenoid

Tetragonal, trigonal and hexagonal prisms

Tetragonal, trigonal and hexagonal pyramids

Tetragonal, trigonal and hexagonal dipyramids

Tetragonal, trigonal and hexagonal salenohedron and trapezohedrons Tetragonal trapezohedron Tetragonal disphenoid Dietragonal scalenohedron Trigonal disphenoid Trigonal trapezohedron Hexagonal scalenohedron Hexagonal trapezohedron

Cubic point groups a2 a3 a1 Example point group: 4/m32/m Symmetry element: three four-fold axes parallel to the coordinate axes, four three-fold rotoinversion axes parallel to room diagonal directions, six two-fold axes, mirrors perpendicular to all two- and four-fold rotation axes Characteristic forms: cube, octahedron, dodecahedron, tetrahexahedron, trapezohedron, trisoctahedron , hexoctahedron h k l, (s. sep. page) a3 a2 a1

Isometric (cubic) crystal form I cube tetrahedron octahedron dodecahedron Trisoctahedron tetrahexahedron trapezohedrons http://www.rockhounds.com/rockshop/xtal/part2.html

Isometric (cubic) crystal form II hexoctahedron tristetrahedron hextetrahedron deltoid dodecahedron gyroids pentagondodecahedron diploid or pyritohedron

Cubic crystals I Spessartine garnet Mn3Al2Si3O12. Haramosh Mountains Baltistan, Northern Areas, Pakistan. The crystal shape is a trapezohedron. Diamonds, C, South Africa. Point group: 4/m3bar2/m. Average crystal size: 1cm. Crystal shape: top row and first crystal in the bottom row: octahedron; middle crystal in bottom row: tetrahedron,; third crystal bottom row: two intergrown octahedra. http://webmineral.brgm.fr:8003

Cubic crystals II Grossular garnet Ca3Al2Si3O12, Jeffrey Quarry, Asbestos, Quebec, Canada. Crystal size: 12 mm. Point group: 4/m3bar2/m. The crystal shape is a dodecahedron. The faces show growth steps. Pyrite FeS2 encased in a very fine-grained sedimentary marlstone (clay and calcite). Navajun-(La Rioja)-Spain. Crystal size: 1-2cm. Point group: 2/m3bar. The striation on the cube faces indicate that the microsciopic symmetry is less than 4/m3bar2/m

Steno's law One property of crystals, that remains constant in all specimens, is the angle between two defined faces. The law of contant interfacial angles is called Steno’s law. The presence or absence of specific faces and the relative size of the indivual faces, however, can be different from specimen to specimen of the same crystal. Shapes typical for a mineral (and location) are called habitus. face missing The first four shapes are hexagons, with an angle of 120° between adjacent faces. Different is the size of each of the individual faces. The last shape is a pentagon, which can be interpreted as hexagon with a missing face.

Quartz crystals Faces (forms) which may be developped are: two trigonal prisms = hexagonal prism (m1, m2), the principal rhombohedron r, the inverse rhombohedron z, a trigonal bipyramid s and a trigonal trapezohedron x, an elongated (acute) rhombohedron (green, f), an acute inverse rhombohedron (yellow, -f), and an acute (negative) trapezohedron (violet, u). The number of forms and their relative size (=habitus) differs according to the physico-chemical conditions in which the crystals were formed. www.faden.it

Habitus in quartz Smoky quartz with prismatic habitus The forms r, z and m1 and m2 are developped (Dôme de Miage) Citrine (yellow quartz) with Tessin habitus The acute rhombohedron f is strongly developped, the rhombohedra r and z are strongly reduced (Arbola). http://www.faden.it/