Euclidean geometry | Symmetry

Crystal system

In crystallography, a crystal system is a set of point groups (a group of geometric symmetries with at least one fixed point). A lattice system is a set of Bravais lattices. Space groups are classified into crystal systems according to their point groups, and into lattice systems according to their Bravais lattices. Crystal systems that have space groups assigned to a common lattice system are combined into a crystal family. The seven crystal systems are triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic. Informally, two crystals are in the same crystal system if they have similar symmetries (albeit there are many exceptions). (Wikipedia).

Crystal system
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Crystal systems and Bravais Lattices

When you consider different unit cell shapes (crystal systems) and centering options you end up with Bravias Lattices. There are 7 crystal systems including cubic, hexagonal, orthorhombic, tetragonal, monoclinic, trigonal, and triclinic. There are four centering possibilities including sim

From playlist Materials Sciences 101 - Introduction to Materials Science & Engineering 2020

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From playlist General Chemistry

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From playlist Intro to Linear Systems

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From playlist CHEMISTRY 16 LIQUIDS AND SOLIDS

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From playlist Atomic Structures and Bonding

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From playlist Intro to Linear Systems

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Crystal lattice and unit cell

All crystalline materials have 3D, long range, periodic order. Therefore, they have a lattice which is a grid of repeating atomic positions. We can pick a small repeating area in this grid and it becomes a unit cell. The primitive unit cell should be the smallest repeatable unit cell.

From playlist Materials Sciences 101 - Introduction to Materials Science & Engineering 2020

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From playlist Linear Algebra

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From playlist Intro to Linear Systems

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From playlist FRUSTRATED METALS AND INSULATORS (HYBRID, 2022)

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From playlist AATRN 2021

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From playlist IIT Kanpur: Nanostructures and Nanomaterials | CosmoLearning.org

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Related pages

Translational symmetry | Klein four-group | Point group | Crystallography | Lattice (group) | Hexagonal lattice | Crystallographic point group | Tetrakis hexahedron | Disdyakis dodecahedron | Symmetric group | Space group | Bravais lattice | Alternating group | Square lattice | Chirality (chemistry) | Symmetry number | Pyramid (geometry) | Orbifold notation | Rotational symmetry | Quasicrystal | Symmetry group | Dihedral group | Point groups in three dimensions | Prism (geometry) | Integer | Reflection symmetry | Group theory | Cyclic group | Rectangular lattice | Polar point group | Oblique lattice | Coxeter notation | Fundamental domain | Cubic crystal system | Geometry | Schoenflies notation