What are the 230 space groups in solid state physics?

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SUMMARY

The discussion centers on the enumeration of the 230 space groups in solid state physics, which represent all possible symmetry operations that leave atomic positions unchanged. This classification is essential for understanding crystal structures and their properties. The reference to the Wikipedia page on space groups provides a comprehensive overview of these groups, which are crucial for researchers in materials science and condensed matter physics.

PREREQUISITES
  • Understanding of symmetry operations in crystallography
  • Familiarity with solid state physics concepts
  • Knowledge of group theory
  • Basic comprehension of crystal structures
NEXT STEPS
  • Research the mathematical foundations of group theory as applied to crystallography
  • Explore the classification of space groups using the International Tables for Crystallography
  • Study the implications of space groups on material properties and behaviors
  • Learn about the application of space groups in computational materials science
USEFUL FOR

Researchers in solid state physics, crystallographers, materials scientists, and students studying the symmetry and properties of crystalline materials will benefit from this discussion.

MathematicalPhysicist
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It's written in one book I've got on solid state physics the following:
If one sought to study nature at the atomic scale and enumerated all the possible symmetry operations, keeping unchanged the positions of atoms (position symmetry), the number of possibilities is 230, making up what are known as the space groups.

Can someone please explain how to get this number of 230 combinatorially?
Thanks!
 
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