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A real rhombic dodecahedron: morphology and crystal shape variations
D G Stepenshchikov1, A D Pavlushin2
1Geological Institute, FRC KSC RAS, Apatity, Russian Federation.
Summary
This study introduces a new geometric method to classify rhombic dodecahedron crystals based on facet distances and edge lengths. It identifies 34 distinct crystal types and their shape variations, aiding in analyzing crystal morphology.
Area of Science:
- Crystallography
- Materials Science
- Geometric Analysis
Background:
- Crystals often exhibit complex morphologies.
- Rhombic dodecahedra are a significant crystallographic form.
- Understanding crystal shape variations is crucial for materials science.
Purpose of the Study:
- To develop a novel geometric characterization method for rhombic dodecahedra.
- To classify distinct rhombic dodecahedral crystal types.
- To determine the range of shape variations for each type.
Main Methods:
- Utilizing distances between parallel facets.
- Measuring lengths of false edges resulting from anisotropic growth.
- Employing minimal-volume circumscribed ellipsoids to define shape variations.
Main Results:
- Identified 34 combinatorially distinct, full-faceted rhombic dodecahedra.
- Determined shape variation ranges for each type using semi-axial lengths.
- Found that 8 special forms cannot exhibit bidirectional isometric tabular morphologies.
Conclusions:
- The method provides tools for precise rhombic dodecahedral crystal morphology analysis.
- Establishes correlations between crystal distortions and environmental dissymmetry.
- Relevant for typomorphic analysis of natural and synthetic crystals like diamonds and garnets.
Keywords:
combinatorial crystallographycrystal shapemorphological analysisreal crystal formrhombic dodecahedronMore Related Videos
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