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A drawing of a butterfly with bilateral symmetry, with left and right sides as mirror images of each other.. In geometry, an object has symmetry if there is an operation or transformation (such as translation, scaling, rotation or reflection) that maps the figure/object onto itself (i.e., the object has an invariance under the transform). [1]
This drawing of the Petersen graph displays a subgroup of its symmetries, isomorphic to the dihedral group D 5, but the graph has additional symmetries that are not present in the drawing. For example, since the graph is symmetric , all edges are equivalent.
The triskelion has 3-fold rotational symmetry. A geometric shape or object is symmetric if it can be divided into two or more identical pieces that are arranged in an organized fashion. [5] This means that an object is symmetric if there is a transformation that moves individual pieces of the object, but doesn't change the overall shape.
Symmetry occurs not only in geometry, but also in other branches of mathematics. Symmetry is a type of invariance: the property that a mathematical object remains unchanged under a set of operations or transformations. [1] Given a structured object X of any sort, a symmetry is a mapping of the object onto itself which preserves the structure.
Asymmetry is the absence of, or a violation of, symmetry (the property of an object being invariant to a transformation, such as reflection). [1] Symmetry is an important property of both physical and abstract systems and it may be displayed in precise terms or in more aesthetic terms. [2]
Rotational symmetry of order n, also called n-fold rotational symmetry, or discrete rotational symmetry of the n th order, with respect to a particular point (in 2D) or axis (in 3D) means that rotation by an angle of (180°, 120°, 90°, 72°, 60°, 51 3 ⁄ 7 °, etc.) does not change the object. A "1-fold" symmetry is no symmetry (all ...
In mathematics, a symmetry operation is a geometric transformation of an object that leaves the object looking the same after it has been carried out. For example, a 1 ⁄ 3 turn rotation of a regular triangle about its center, a reflection of a square across its diagonal, a translation of the Euclidean plane, or a point reflection of a sphere through its center are all symmetry operations.
C 1 is the trivial group containing only the identity operation, which occurs when the figure is asymmetric, for example the letter "F". C 2 is the symmetry group of the letter "Z", C 3 that of a triskelion, C 4 of a swastika, and C 5, C 6, etc. are the symmetry groups of similar swastika-like figures with five, six, etc. arms instead of four.