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A circle is thus said to be symmetric under rotation or to have rotational symmetry. If the isometry is the reflection of a plane figure about a line, then the figure is said to have reflectional symmetry or line symmetry; [3] it is also possible for a figure/object to have more than one line of symmetry. [4]
Rank 3 groups Other names Example geometry Example finite subgroups; O(3) Full symmetry of the sphere [3,3] = , [4,3] = , [5,3] = [4,3 +] = SO(3) Sphere group: Rotational symmetry [3,3] + = , [4,3] + = , [5,3] + = O(2)×O(1) O(2)⋊C 2: Dih ∞ ×Dih 1 Dih ∞ ⋊C 2: Full symmetry of a spheroid, torus, cylinder, bicone or hyperboloid Full ...
Lists of shapes cover different types of geometric shape and related topics. They include mathematics topics and other lists of shapes, such as shapes used by drawing or teaching tools. They include mathematics topics and other lists of shapes, such as shapes used by drawing or teaching tools.
That is, a figure which does not change upon undergoing a reflection has reflectional symmetry. In 2-dimensional space, there is a line/axis of symmetry, in 3-dimensional space, there is a plane of symmetry. An object or figure which is indistinguishable from its transformed image is called mirror symmetric. In conclusion, a line of symmetry ...
The order of the symmetry group is the number of symmetries of the polyhedron. One often distinguishes between the full symmetry group, which includes reflections, and the proper symmetry group, which includes only rotations. The symmetry groups of the Platonic solids are a special class of three-dimensional point groups known as polyhedral ...
There is no geometric figure that has as full symmetry group the circle group, but for a vector field it may apply (see the three-dimensional case below). the orthogonal group O(2) consisting of all rotations about a fixed point and reflections in any axis through that fixed point. This is the symmetry group of a circle.
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