Concepts inPartial intrinsic reflectional symmetry of 3D shapes
Reflection symmetry
Reflection symmetry, reflectional symmetry, line symmetry, mirror symmetry, mirror-image symmetry, or bilateral symmetry is symmetry with respect to reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry. In 2D there is a line of symmetry, in 3D a plane of symmetry. An object or figure which is indistinguishable from its transformed image is called mirror symmetric. Also see pattern.
more from Wikipedia
Shape
The shape (Old English: gesceap, created thing) of an object located in some space is a geometrical description of the part of that space occupied by the object, as determined by its external boundary ¿ abstracting from location and orientation in space, size, and other properties such as colour, content, and material composition.
more from Wikipedia
Rotational symmetry
Generally speaking, an object with rotational symmetry is an object that looks the same after a certain amount of rotation. An object may have more than one rotational symmetry; for instance, if reflections or turning it over are not counted, the triskelion appearing on the Isle of Man's flag (see opposite) has three rotational symmetries (or "a threefold rotational symmetry"). More examples may be seen below.
more from Wikipedia
Symmetry
Symmetry (from Greek ¿¿¿¿¿¿¿¿¿¿ symmetría "measure together") generally conveys two primary meanings. The first is an imprecise sense of harmonious or aesthetically pleasing proportionality and balance; such that it reflects beauty or perfection. The second meaning is a precise and well-defined concept of balance or "patterned self-similarity" that can be demonstrated or proved according to the rules of a formal system: by geometry, through physics or otherwise.
more from Wikipedia
Scalar field
In mathematics and physics, a scalar field associates a scalar value to every point in a space. The scalar may either be a mathematical number, or a physical quantity. Scalar fields are required to be coordinate-independent, meaning that any two observers using the same units will agree on the value of the scalar field at the same point in space (or spacetime).
more from Wikipedia
Global symmetry
A global symmetry is a symmetry that holds at all points in the spacetime under consideration, as opposed to a local symmetry which varies from point to point. Global symmetries require conservation laws, but not forces, in physics. An example of a global symmetry is the action of the (for a constant - making it a global transformation) group on the Dirac Lagrangian: Under this transformation the wavefunction changes as and and so clearly:
more from Wikipedia
Three-dimensional space
Three-dimensional space is a geometric 3-parameters model of the physical universe (without considering time) in which we live. These three dimensions are commonly called length, width, and depth (or height), although any three directions can be chosen, provided that they do not lie in the same plane. In physics and mathematics, a sequence of n numbers can be understood as a location in n-dimensional space. When n = 3, the set of all such locations is called 3-dimensional Euclidean space.
more from Wikipedia
Manifold
In mathematics, a manifold is a mathematical object that on a small enough scale resembles Euclidean space. For example, seen from far away, the surface of the planet Earth is not flat and Euclidean, but on a smaller scale, one may describe each region via a geographic map, a projection of the surface onto the Euclidean plane. A precise mathematical definition of a manifold is given below. Lines and circles (but not figure eights) are one-dimensional manifolds (1-manifolds).
more from Wikipedia