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Types of Symmetry

Double Rotation Symmetry
Double Rotation Symmetry

In 4D, a double rotation symmetry can be generated as the composite of two orthogonal rotations. It is similar to 3D screw axis which is the composite of a rotation and an orthogonal translation. Non-isometric symmetries. A wider definition of geometric symmetry allows operations from a larger group than the Euclidean group of isometries.

Double Rotation Symmetry
Double Rotation Symmetry

In 4D, a double rotation symmetry can be generated as the composite of two orthogonal rotations. It is similar to 3D screw axis which is the composite of a rotation and an orthogonal translation. Non-isometric symmetries. A wider definition of geometric symmetry allows operations from a larger group than the Euclidean group of isometries.

Euclidean Symmetries in General
Euclidean Symmetries in General

Symmetry (geometry) A drawing of a butterfly with bilateral symmetry, with left and right sides as mirror images of each other. ... Euclidean symmetries in general Edit.

Glide Reflection Symmetry
Glide Reflection Symmetry

In the case of glide reflection symmetry, the symmetry group of an object contains a glide reflection, and hence the group generated by it.

Helical Symmetry
Helical Symmetry

In spiral or helical symmetry, the architectural piece exhibits a spiral or helix. In other words, there is a central vertical axis that the architectural piece "winds" around and either toward or away from. This special type of similarity symmetry expresses a theme of continuity.

Point Reflection and Other Involutive Isometries
Point Reflection and Other Involutive Isometries

Point reflection and other involutive isometries. Reflection ... That's why in physics the term "P-symmetry" is used for both point reflection and mirror symmetry ...

Reflectional Symmetry
Reflectional Symmetry

Reflectional symmetry occurs when a line is used to split an object or shape in halves so that each half reflects the other half. Sometimes objects or shapes have more than one line of symmetry. Take, for instance, the letter H.

source: study.com
Rotational Symmetry
Rotational Symmetry

Rotational symmetry, also known as radial symmetry in biology, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which it looks the same.

Translational Symmetry
Translational Symmetry

In geometry, a translation "slides" a thing by a: T a (p) = p + a. In physics and mathematics, continuous translational symmetry is the invariance of a system of equations under any translation. Discrete translational symmetry is invariant under discrete translation.

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