odd isometry
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Euclidean plane isometry — In geometry, a Euclidean plane isometry is an isometry of the Euclidean plane, or more informally, a way of transforming the plane that preserves geometrical properties such as length. There are four types: translations, rotations, reflections,… … Wikipedia
Dade isometry — In mathematical finite group theory, the Dade isometry is an isometry from class functions on a subgroup H with support on a subset K of H to class functions on a group G (Collins 1990, 6.1). It was introduced by Dade (1964) as a generalization… … Wikipedia
Hjelmslev's theorem — In geometry, Hjelmslev s theorem, named after Johannes Hjelmslev, is the statement that if points P, Q, R... of one and the same line are isometrically mapped to points P´, Q´, R´... of another line in the same plane, then the midpoints of the… … Wikipedia
Point groups in three dimensions — In geometry, a point group in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry group of a sphere. It is a subgroup of the orthogonal group O(3), the group of all isometries… … Wikipedia
Dihedral group — This snowflake has the dihedral symmetry of a regular hexagon. In mathematics, a dihedral group is the group of symmetries of a regular polygon, including both rotations and reflections.[1] Dihedr … Wikipedia
Point groups in two dimensions — In geometry, a point group in two dimensions is an isometry group in two dimensions that leaves the origin fixed, or correspondingly, an isometry group of a circle. It is a subgroup of the orthogonal group O(2), the group of all isometries which… … Wikipedia
Conjugation of isometries in Euclidean space — In a group, the conjugate by g of h is ghg−1. Contents 1 Translation 2 Inversion 3 Rotation 4 Reflection … Wikipedia
Rotation matrix — In linear algebra, a rotation matrix is a matrix that is used to perform a rotation in Euclidean space. For example the matrix rotates points in the xy Cartesian plane counterclockwise through an angle θ about the origin of the Cartesian… … Wikipedia
Small cancellation theory — In the mathematical subject of group theory, small cancellation theory studies groups given by group presentations satisfying small cancellation conditions, that is where defining relations have small overlaps with each other. It turns out that… … Wikipedia
Feit–Thompson theorem — In mathematics, the Feit–Thompson theorem, or odd order theorem, states that every finite group of odd order is solvable. It was proved by Walter Feit and John Griggs Thompson (1962, 1963) Contents 1 History 2 Significance of the proof … Wikipedia
Crystallographic restriction theorem — The crystallographic restriction theorem in its basic form was based on the observation that the rotational symmetries of a crystal are usually limited to 2 fold, 3 fold, 4 fold, and 6 fold. However, quasicrystals can occur with other symmetries … Wikipedia
