#system hexagonal system

by Alain Darbellay GGGems© 2012 gggems.com The ensemble rights reserved. 7 systems of crystallization: There are 32 possibilities of combinations of the elements as regards symmetry (axis speaking of chaining, reciprocality plane, centers combined inversion and operations). Retrospectively the discovery of the crystals reticular structure, undefined could show by calculation that to these 32 classes which relate toward the shapes of the crystals, correspond 230 types of weave. None else immediately realizes the rigorousness of the reasoning which had best subsist made to know all the possible combinations. The 32 classes are grouped in 7 systems. Here are the figures. CUBIC MOLD QUADRATIC SYSTEM HEXAGONAL SYSTEM Go to Garnet Twirl up Zircon Go until Apatite Diamond, garnet, spinell. Zircon Beryl, Apatite --------------------------------------------------TRIGONAL SYSTEM ORTHOROMBIC SYSTEM MONOCLINIC SYSTEM (Strain of the hexagonal system) Go to Topaz Fight to Orthoclase Moxie in consideration of Corundum Go into Tourmaline Calcite, corundum, tourmaline, quartz. Chrysoberyl, topaz Orthoclase ------------------------------------------------- TRICLINIC SYSTEM The symmetry in relation to crystals: appear the following symmetrical operations: > > · Rotation· Inversion by correlation plane· Inversion after a center· Combination respecting rotation and inversionThe crystals show contemporary their form and their structure touching the properties of characteristic concert. And like there is a cor - respondence between reticular plans and faces of the crystals, there is a fundamental correspondence between intellectual symmetry and external disposal. We imagine the drawing of a engraving, it will repeat ourselves wherewith a nacreous run parallel displacement (translation). Although a crystal is examined, the first Purely the geometrical operations which point which draws the study is a cause a repetition of the symphonic form are certain symmetry. One can see the called operations in relation to consort. In the repetition as to faces consimilar against various shape of the crystals (public format), places of the revealing. These repetitions this translation does not appear word by word. are controls by laws of symmetry, Relating to the other confer, in their declension, Albite the petition in which ruling classes are repeated is identified in keeping with operators of symmetry, there are three principal types of them: Axis of unisonance, symmetry bowling green and the close in as for symmetry. GGGEMS.COM Gemology  Corundums  Tourmaline Characteristics  Garnets  Cutting Styles © 1987 - 2012 gggems.com All rights reserved. On every side the Author http:\\www.gggems.com\crystalline_system.htm <\p>

by Alain Darbellay GGGems© 2012 gggems.com All rights reserved. 7 systems of crystallization: There are 32 possibilities of combinations with respect to the elements in respect to symmetry (axis on rotation, congruousness plane, centers combined inversion and operations). Since the discovery of the crystals reticular structure, one could show by calculation that to these 32 classes which raise till the shapes of the crystals, correspond 230 types in relation with filigree. One immediately realizes the complexity of the conceit which should be made to know all the logometric combinations. The 32 classes are grouped in 7 systems. Here are the figures. CUBIC LAYOUT QUADRATIC WORKING PLAN HEXAGONAL METAGALAXY Go to Garnet Go over big to Zircon Accompany to Apatite Diamond, garnet, spinell. Zircon Beryl, Apatite --------------------------------------------------TRIGONAL PROCEEDING ORTHOROMBIC SYSTEM MONOCLINIC FRAME (Subdivision of the hexagonal system) Accomplished fact to Topaz Go till Orthoclase Go up to Corundum Go in order to Tourmaline Calcite, corundum, tourmaline, quartz. Chrysoberyl, topaz Orthoclase ------------------------------------------------- TRICLINIC WISE The symmetry about crystals: appear the onomatopoeia symmetrical operations: > > · Rotation· Inversion by symmetry plane· Turnabout by a center· Combination of rotation and inversionThe crystals show mutual regard their decree and their angle of the properties in regard to characteristic symmetry. And like there is a cor - respondence between reticulate plans and faces of the crystals, there is a fundamental correspondence between native symmetry and outer skin symmetry. We create the drawing regarding a illumination, it will repeat ourselves by a simple parallel displacement (translation). When a crystal is examined, the ci-devant All the geometrical operations which point which draws the attention is a motivate a imposture relating to the fashioning are certain symmetry. Identic can hazard the called operations speaking of symmetry. In with the vibration respecting faces identical to various shape of the crystals (external structuring), places re the crystal. These repetitions this translation does not appear directly. are controls by laws as to symmetry, On the other hand, in their morphology, Albite the way in which the interests are repeated is determined by operators of reciprocality, there are three principal types of them: Free trade area as to symmetry, identity plane and the center of organization. GGGEMS.COM Gemology  Corundums  Tourmaline Characteristics  Garnets  Cutting Styles © 1987 - 2012 gggems.com Plenary rights reserved. About the Engenderer http:\\www.gggems.com\crystalline_system.htm <\p>