Group theory and generalizations Concept
Symmetry group
Summary
The symmetry group of an object is the group of all transformations of the ambient space that map the object onto itself. These transformations must keep the relevant structure of the object. The operation is composition of transformations. It is often written for an object .
Remarks
The symmetry group of a regular -gon in the plane is the dihedral group of order . The rotations of a regular tetrahedron form a group isomorphic to the alternating group . The symmetry group of an object is a subgroup of the group of all transformations of the ambient space.
Where this leads
7 pages build on this one.
Further reading
- Web https://en.wikipedia.org/wiki/Symmetry_group, lead section
- Web https://en.wikipedia.org/wiki/Symmetry_group, Symmetry groups in general
About this page
| Tag | 0ZG3Z5JZ85 |
|---|---|
| URI | m2://0ZG3Z5JZ85 |
| Kind | concept |
| Writing | W1 stated |
| MSC | 20B25 |
| Specializes | Group |
| Same as |
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What this page needs for W2
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- edge not_instance_of in: at least one non-example (0 of 1)
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