In geometry, a point group in four dimensions is an isometry group in four dimensions that leaves the origin fixed, or correspondingly, an isometry group...

In geometry, a point group in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry...

181440. Point groups in two dimensions Point groups in three dimensions Point groups in four dimensions Crystallography Crystallographic point group Molecular...

restriction theorem). Point group Point groups in three dimensions Point groups in four dimensions One-dimensional symmetry group Solomon, Ronald (2003)...

In geometry, dihedral symmetry in three dimensions is one of three infinite sequences of point groups in three dimensions which have a symmetry group...

distinct. Space groups are discrete cocompact groups of isometries of an oriented Euclidean space in any number of dimensions. In dimensions other than 3...

of the world is a four-dimensional space but not the one that was found necessary to describe electromagnetism. The four dimensions (4D) of spacetime...

mirror planes remain unchanged. Molecular symmetry Point group Space group Point groups in three dimensions Crystal system Authier, André (2015). "12. The...

Schoenflies, is a notation primarily used to specify point groups in three dimensions. Because a point group alone is completely adequate to describe the symmetry...

of the dihedral groups, one more for the positions of the mirrors. The remaining isometry groups in two dimensions with a fixed point are: the special...

In three dimensional geometry, there are four infinite series of point groups in three dimensions (n≥1) with n-fold rotational or reflectional symmetry...

spaces, of four or fewer dimensions. Representative topics are the theory of 3-manifolds and 4-manifolds, knot theory, and braid groups. This can be regarded...

and 1973. It has been refined since. The original theory proposed four dimensions along which cultural values could be analyzed: individualism-collectivism;...

phase space with six dimensions, too many to plot but they can be analysed mathematically. The rotation group in four dimensions, SO(4), has six degrees...

lattices and point groups. It is formed by combining crystal systems that have space groups assigned to a common lattice system. In three dimensions, the hexagonal...

A general rotation in four dimensions has only one fixed point, the centre of rotation, and no axis of rotation; see rotations in 4-dimensional Euclidean...

space. The 14 possible symmetry groups of Bravais lattices are 14 of the 230 space groups. In the context of the space group classification, the Bravais lattices...

table Crystallographic point group Molecular geometry Point groups in three dimensions Symmetry of diatomic molecules Symmetry in quantum mechanics Woodward...

Inventions & Dimensions is the third album by Herbie Hancock, recorded on August 30, 1963, for Blue Note Records. It features Hancock with bassist Paul...

Lego Dimensions is a Lego-themed action-adventure platform crossover video game developed by Traveller's Tales and published by Warner Bros. Interactive...

examples of Lie groups and other related topics see the list of simple Lie groups; the Bianchi classification of groups of up to three dimensions; see classification...

symmetries have all discrete prismatic symmetries, Dnh as subgroups. In four dimensions, an object can have circular symmetry, on two orthogonal axis planes...

of simple groups*; they provide a linear representation of the group of rotations in a space with any number n {\displaystyle n} of dimensions, each spinor...

In mathematics, a rotation of axes in two dimensions is a mapping from an xy-Cartesian coordinate system to an x′y′-Cartesian coordinate system in which...

four-dimensional analogues of the regular polyhedra in three dimensions and the regular polygons in two dimensions. There are six convex and ten star regular 4-polytopes...

include the great dirhombicosidodecahedron in three dimensions and the grand antiprism in four dimensions. Equivalently, the Wythoffian polytopes can...

In precise topological terms, each point of the 3-sphere has a neighborhood which is homeomorphic to an open subset of 3-D space. In three dimensions...

tablet fragments from villains within their respective dimensions. Gameplay alternates between the four Spider-Men, who control similarly but present a different...

orthogonal group: O(2). The following table gives examples of rotation and reflection matrix : In mathematics, a rotation of axes in two dimensions is a mapping...

finite simple groups that arise from four general families of such groups: Two general groups stem from cyclic groups and alternating groups. Sixteen families...