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Law Of Symmetry (crystallography)
The law of symmetry is a law in the field of crystallography concerning crystal structure. The law states that all crystals of the same substance possess the same elements of symmetry. The law is also named the ''law of constancy of symmetry'', ''René Just Haüy, Haüy's law'' or the ''third law of crystallography''. Definition The way in which the law of symmetry was originally defined by Haüy in 1815 was based on his law of rational indices, law of decrements and his conception of crystals being assembled of tiny parallelepipeds (''molécules intégrantes'') stacked up in three dimensions without leaving any gaps. The modern definition of the law of symmetry is based on symmetry elements, and is more in the German dynamistic crystallographic tradition of Christian Samuel Weiss, Moritz Ludwig Frankenheim and Johann F. C. Hessel. Weiss and his followers studied the external symmetry of crystals rather than their internal structure. René Just Haüy first lectured about his la ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reflection Symmetry
In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a Reflection (mathematics), reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry. In Two-dimensional space, two-dimensional space, there is a line/axis of symmetry, in Three-dimensional space, three-dimensional space, there is a plane (mathematics), plane of symmetry. An object or figure which is indistinguishable from its transformed image is called mirror image, mirror symmetric. Symmetric function In formal terms, a mathematical object is symmetric with respect to a given mathematical operation, operation such as reflection, Rotational symmetry, rotation, or Translational symmetry, translation, if, when applied to the object, this operation preserves some property of the object. The set of operations that preserve a given property of the object form a group (algebra), group. Two objects are symmetr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tetrahedral Symmetry
image:tetrahedron.svg, 150px, A regular tetrahedron, an example of a solid with full tetrahedral symmetry A regular tetrahedron has 12 rotational (or orientation-preserving) symmetries, and a symmetry order of 24 including transformations that combine a reflection and a rotation. The group of all (not necessarily orientation preserving) symmetries is isomorphic to the group S4, the symmetric group of permutations of four objects, since there is exactly one such symmetry for each permutation of the vertices of the tetrahedron. The set of orientation-preserving symmetries forms a group referred to as the alternating group, alternating subgroup A4 of S4. Details Chiral and full (or achiral tetrahedral symmetry and pyritohedral symmetry) are Point groups in three dimensions, discrete point symmetries (or equivalently, List of spherical symmetry groups, symmetries on the sphere). They are among the Crystal system#Overview of point groups by crystal system, crystallographic point gro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tourmalines
Tourmaline ( ) is a crystalline silicate mineral group in which boron is compounded with elements such as aluminium, iron Iron is a chemical element; it has symbol Fe () and atomic number 26. It is a metal that belongs to the first transition series and group 8 of the periodic table. It is, by mass, the most common element on Earth, forming much of Earth's o ..., magnesium, sodium, lithium, or potassium. This gemstone comes in a wide variety of colors. The name is derived from the Sinhala language, Sinhalese (), which refers to the carnelian gemstones. History Brightly colored Ceylonese gem tourmalines were brought to Europe in great quantities by the Dutch East India Company to satisfy a demand for curiosities and gems. Tourmaline was sometimes called the "Ceylonese Magnet" because it could attract and then repel hot ashes due to its Pyroelectricity, pyroelectric properties. Tourmalines were used by chemists in the 19th century to Polarization (waves), polariz ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quartz
Quartz is a hard, crystalline mineral composed of silica (silicon dioxide). The Atom, atoms are linked in a continuous framework of SiO4 silicon–oxygen Tetrahedral molecular geometry, tetrahedra, with each oxygen being shared between two tetrahedra, giving an overall chemical formula of Silicon dioxide, SiO2. Quartz is, therefore, classified structurally as a Silicate mineral#Tectosilicates, framework silicate mineral and compositionally as an oxide mineral. Quartz is the second most abundant mineral in Earth's continental crust, behind feldspar. Quartz exists in two forms, the normal α-quartz and the high-temperature β-quartz, both of which are chiral. The transformation from α-quartz to β-quartz takes place abruptly at . Since the transformation is accompanied by a significant change in volume, it can easily induce microfracturing of ceramics or rocks passing through this temperature threshold. There are many different varieties of quartz, several of which are classifi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boracite
Boracite is a magnesium borate mineral with formula: Mg3 B7 O13 Cl. It occurs as blue green, colorless, gray, yellow to white crystals in the orthorhombic - pyramidal crystal system. Boracite also shows pseudo-isometric cubical and octahedral forms. These are thought to be the result of transition from an unstable high temperature isometric form on cooling. Penetration twins are not unusual. It occurs as well formed crystals and dispersed grains often embedded within gypsum and anhydrite crystals. It has a Mohs hardness of 7 to 7.5 and a specific gravity of 2.9. Refractive index values are nα = 1.658 - 1.662, nβ = 1.662 - 1.667 and nγ = 1.668 - 1.673. It has a conchoidal fracture and does not show cleavage. It is insoluble in water (not to be confused with borax, which is soluble in water). Boracite is typically found in evaporite sequences associated with gypsum, anhydrite, halite, sylvite, carnallite, kainite and hilgardite. It was first described in 1789 for specimens f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cube To Tetrahedron (hemihedry)
A cube or regular hexahedron is a three-dimensional solid object in geometry, which is bounded by six congruent square faces, a type of polyhedron. It has twelve congruent edges and eight vertices. It is a type of parallelepiped, with pairs of parallel opposite faces, and more specifically a rhombohedron, with congruent edges, and a rectangular cuboid, with right angles between pairs of intersecting faces and pairs of intersecting edges. It is an example of many classes of polyhedra: Platonic solid, regular polyhedron, parallelohedron, zonohedron, and plesiohedron. The dual polyhedron of a cube is the regular octahedron. The cube can be represented in many ways, one of which is the graph known as the cubical graph. It can be constructed by using the Cartesian product of graphs. The cube is the three-dimensional hypercube, a family of polytopes also including the two-dimensional square and four-dimensional tesseract. A cube with unit side length is the canonical unit of volume in t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rhombohedron
In geometry, a rhombohedron (also called a rhombic hexahedron or, inaccurately, a rhomboid) is a special case of a parallelepiped in which all six faces are congruent rhombi. It can be used to define the rhombohedral lattice system, a honeycomb with rhombohedral cells. A rhombohedron has two opposite apices at which all face angles are equal; a prolate rhombohedron has this common angle acute, and an oblate rhombohedron has an obtuse angle at these vertices. A cube is a special case of a rhombohedron with all sides square. Special cases The common angle at the two apices is here given as \theta. There are two general forms of the rhombohedron: oblate (flattened) and prolate (stretched). In the oblate case \theta > 90^\circ and in the prolate case \theta < 90^\circ. For the figure is a cube. Certain proportions of the rhombs give rise to some well-known special cases. These typically occur in both prolate and oblate forms. ...
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Law Of Constancy Of Interfacial Angles
The law of constancy of interfacial angles (; ) is an Empirical research, empirical law in the fields of crystallography and mineralogy concerning the shape, or morphology, of crystals. The law states that the angles between adjacent corresponding faces of crystals of a particular substance are always constant despite the different shapes, sizes, and mode of growth of crystals. The law is also named the ''first law of crystallography'' or ''Nicolas Steno, Steno's law''. Definition The International Union of Crystallography (IUCr) gives the following definition: "The law of the constancy of interfacial angles (or 'first law of crystallography') states that the angles between the crystal faces of a given species are constant, whatever the lateral extension of these faces and the origin of the crystal, and are characteristic of that species." The law is valid at constant temperature and pressure. This law is important in identifying different mineral species as small changes in at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Improper Rotation
In geometry, an improper rotation. (also called rotation-reflection, rotoreflection, rotary reflection,. or rotoinversion) is an isometry in Euclidean space that is a combination of a Rotation (geometry), rotation about an axis and a reflection (mathematics), reflection in a plane perpendicular to that axis. Reflection and Point reflection, inversion are each a special case of improper rotation. Any improper rotation is an affine transformation and, in cases that keep the coordinate origin fixed, a linear transformation.. It is used as a symmetry operation in the context of Symmetry (geometry), geometric symmetry, molecular symmetry and Crystallographic point group, crystallography, where an object that is unchanged by a combination of rotation and reflection is said to have ''improper rotation symmetry''. Three dimensions In 3 dimensions, improper rotation is equivalently defined as a combination of rotation about an axis and inversion in a point on the axis. For this reason ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
