dbo:abstract
|
- A plane symmetry is a symmetry of a pattern in the Euclidean plane: that is, a transformation of the plane that carries any direction lines to lines and preserves many different distances. If one has a pattern in the plane, the set of plane symmetries that preserve the pattern forms a group. The groups that arise in this way are plane symmetry groups and are of considerable mathematical interest. A symmetry plane is a three-dimensional object's symmetry axe. There are several kinds of plane symmetry groups:
* Reflection groups. These are plane symmetry groups that are generated by reflections, possibly limited to reflections in lines through the origin.
* Rotation groups. These groups consist of rotations around a point.
* Translation groups.
* Symmetries of geometrical figures. Some of these are reflection groups, e.g., the group of symmetries of the square or the rectangle. The symmetry group of a swastika or any similar figure without an axis of symmetry is a rotation group. (en)
|
dbo:wikiPageID
| |
dbo:wikiPageLength
|
- 1393 (xsd:nonNegativeInteger)
|
dbo:wikiPageRevisionID
| |
dbo:wikiPageWikiLink
| |
dbp:wikiPageUsesTemplate
| |
dcterms:subject
| |
gold:hypernym
| |
rdfs:comment
|
- A plane symmetry is a symmetry of a pattern in the Euclidean plane: that is, a transformation of the plane that carries any direction lines to lines and preserves many different distances. If one has a pattern in the plane, the set of plane symmetries that preserve the pattern forms a group. The groups that arise in this way are plane symmetry groups and are of considerable mathematical interest. A symmetry plane is a three-dimensional object's symmetry axe. There are several kinds of plane symmetry groups: (en)
|
rdfs:label
| |
owl:sameAs
| |
prov:wasDerivedFrom
| |
foaf:isPrimaryTopicOf
| |
is dbo:wikiPageRedirects
of | |
is dbo:wikiPageWikiLink
of | |
is foaf:primaryTopic
of | |