symmetroids

Symmetroids are a class of mathematical objects that exhibit a specific type of symmetry. In essence, a symmetroid is a set of points, vectors, or other mathematical entities that remain unchanged under a particular transformation or a group of transformations. This invariance is the defining characteristic. The term "symmetroid" itself is not as widely established as terms like "group" or "manifold," and may appear in specialized literature or specific theoretical frameworks.

The nature of the symmetry in a symmetroid can vary greatly. For example, in geometry, a symmetroid might refer to a shape that looks the same after rotation, reflection, or translation. In linear algebra, a symmetroid could be a matrix that is equal to its transpose, a property known as being symmetric. More abstractly, in group theory, a symmetroid could be a subset of elements within a group that is invariant under conjugation by elements of the group. The precise definition and properties of a symmetroid depend heavily on the context in which the term is used. Often, the underlying structure being considered will dictate the specific type of symmetry operation that defines a symmetroid.