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  2. Crystal system - Wikipedia

    en.wikipedia.org/wiki/Crystal_system

    A crystal system is a set of point groups in which the point groups themselves and their corresponding space groups are assigned to a lattice system. Of the 32 crystallographic point groups that exist in three dimensions, most are assigned to only one lattice system, in which case both the crystal and lattice systems have the same name. However ...

  3. Crystal structure - Wikipedia

    en.wikipedia.org/wiki/Crystal_structure

    The defining property of a crystal is its inherent symmetry. Performing certain symmetry operations on the crystal lattice leaves it unchanged. All crystals have translational symmetry in three directions, but some have other symmetry elements as well. For example, rotating the crystal 180° about a certain axis may result in an atomic ...

  4. Isomorphism (crystallography) - Wikipedia

    en.wikipedia.org/wiki/Isomorphism_(crystallography)

    Forsterite. In chemistry, isomorphism has meanings both at the level of crystallography and at a molecular level. In crystallography, crystals are isomorphous if they have identical symmetry and if the atomic positions can be described with a set of parameters (unit cell dimensions and fractional coordinates) whose numerical values differ only slightly.

  5. Crystallography - Wikipedia

    en.wikipedia.org/wiki/Crystallography

    Before the 20th century, the study of crystals was based on physical measurements of their geometry using a goniometer. [4] This involved measuring the angles of crystal faces relative to each other and to theoretical reference axes (crystallographic axes), and establishing the symmetry of the crystal in question.

  6. Cubic crystal system - Wikipedia

    en.wikipedia.org/wiki/Cubic_crystal_system

    A network model of a primitive cubic system The primitive and cubic close-packed (also known as face-centered cubic) unit cells. In crystallography, the cubic (or isometric) crystal system is a crystal system where the unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in crystals and minerals.

  7. Hermann–Mauguin notation - Wikipedia

    en.wikipedia.org/wiki/Hermann–Mauguin_notation

    These are the crystallographic point groups 1 and 1 (triclinic crystal system), 2, m, and ⁠ 2 / m ⁠ , and 222, ⁠ 2 / m ⁠ ⁠ 2 / m ⁠ ⁠ 2 / m ⁠, and mm2 (orthorhombic). (The short form of ⁠ 2 / m ⁠ ⁠ 2 / m ⁠ ⁠ 2 / m ⁠ is mmm.) If the symbol contains three positions, then they denote symmetry elements in the x, y, z ...

  8. Centrosymmetry - Wikipedia

    en.wikipedia.org/wiki/Centrosymmetry

    In crystallography, a centrosymmetric point group contains an inversion center as one of its symmetry elements. [1] In such a point group, for every point (x, y, z) in the unit cell there is an indistinguishable point (-x, -y, -z). Such point groups are also said to have inversion symmetry. [2] Point reflection is a similar term used in geometry.

  9. Portal:Minerals - Wikipedia

    en.wikipedia.org/wiki/Portal:Minerals

    The crystal structure of pyrite is primitive cubic, and this is reflected in the cubic symmetry of its natural crystal facets. In crystallography, the cubic (or isometric) crystal system is a crystal system where the unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in crystals and minerals.