In general, every kind of structure in mathematics will have its own kind of symmetry, many of which are listed in the given points mentioned above.
https://en.wikipedia.org/wiki/Symmetry_in_mathematics
Reflectional symmetry, mirror symmetry, mirror-image symmetry, or bilateral symmetry is symmetry with respect to reflection. In one dimension, there is a point of symmetry about which reflection takes place; in two dimensions there is an axis of symmetry, and in three dimensions there is a plane of symmetry.
https://en.wikipedia.org/wiki/Symmetry_%28geometry%29
This article describes symmetry from three perspectives: in mathematics, including geometry, the most familiar type of symmetry for many people; in science and nature; and in the arts, covering architecture, art and music.
https://en.wikipedia.org/wiki/Symmetry
In mathematics, symmetry has a more precise definition, that an object is invariant to a transformation, such as reflection but including other transforms too. Although these two meanings of symmetry can sometimes be told apart, they are related, so they are here discussed together.
https://en.wikipedia.org/wiki/Symmetry
Symmetry occurs not only in geometry, but also in other branches of mathematics. Symmetry is a type of invariance: the property that something does not change under a set of transformations. Given a structured object X of any sort, a symmetry is a mapping of the object onto itself which preserves the structure. This occurs in many cases; for example, if X is a set with no additional structure, a symmetry is a bijective map from the set to itself, giving rise to permutation groups.
https://en.wikipedia.org/wiki/Symmetry_in_mathematics
A circle is said to be symmetric under rotation or to have rotational symmetry. If the isometry is the reflection of a plane figure, the figure is said to have reflectional symmetry or line symmetry; moreover, it is possible for a figure/object to have more than one line of symmetry.
https://en.wikipedia.org/wiki/Symmetry_%28geometry%29
1 An object has scale symmetry if it does not change shape when it is expanded or contracted. 2  Fractals also exhibit a form of scale symmetry, where small portions of the fractal are similar in shape to large portions. 3  Other symmetries include glide reflection symmetry and rotoreflection symmetry.
https://en.wikipedia.org/wiki/Symmetry
In another meaning of the word, the rotation group of an object is the symmetry group within E + (m), the group of rigid motions; in other words, the intersection of the full symmetry group and the group of rigid motions.
https://en.wikipedia.org/wiki/Symmetry_%28geometry%29
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https://www.ixl.com/math/grade-3/symmetry
In 2D, a glide reflection symmetry (in 3D it is called a glide plane symmetry, and a transflection in general) means that a reflection in a line or plane combined with a translation along the line / in the plane, results in the same object.
https://en.wikipedia.org/wiki/Symmetry_%28geometry%29
symmetry math definition
In math, symmetry is defined as the property that something does not change under a set of transformations.