In geometry, an object has symmetry if there is an operation or transformation (such as translation, scaling, rotation or reflection) that maps the figure/object...

determines what geometry is. Symmetry in classical Euclidean geometry is represented by congruences and rigid motions, whereas in projective geometry an analogous...

This article describes symmetry from three perspectives: in mathematics, including geometry, the most familiar type of symmetry for many people; in science...

group of the ambient space. This article mainly considers symmetry groups in Euclidean geometry, but the concept may also be studied for more general types...

half the symmetry order of the square. d2 is the symmetry of an isosceles trapezoid, and p2 is the symmetry of a kite. g2 defines the geometry of a parallelogram...

molecular symmetry describes the symmetry present in molecules and the classification of these molecules according to their symmetry. Molecular symmetry is a...

symmetry can also be discrete with a fixed angle of rotation, 360°/n for n-fold symmetry. Axiality (geometry) Circular symmetry Reflection symmetry Rotational...

In algebraic geometry and theoretical physics, mirror symmetry is a relationship between geometric objects called Calabi–Yau manifolds. The term refers...

Rotational symmetry, also known as radial symmetry in geometry, is the property a shape has when it looks the same after some rotation by a partial turn...

Math movement. An exploration of transformation geometry often begins with a study of reflection symmetry as found in daily life. The first real transformation...

(projective geometry, technical drawing, etc.) it is given a more precise definition, which may include either one or two axes of symmetry of an ellipse...

Symmetry occurs not only in geometry, but also in other branches of mathematics. Symmetry is a type of invariance: the property that a mathematical object...

In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure...

further classified as spatial symmetries, involving only the spatial geometry associated with a physical system; temporal symmetries, involving only changes...

In geometry, circular symmetry is a type of continuous symmetry for a planar object that can be rotated by any arbitrary angle and map onto itself. Rotational...

 23. Johnson, Norman W. (2018), Geometries and Transformations, ISBN 978-1-107-10340-5. See Chapter 11: Finite Symmetry Groups, 11.3 Pyramids, Prisms,...

In mathematics, and especially in geometry, an object has icosahedral symmetry if it has the same symmetries as a regular icosahedron. Examples of other...

Absolute geometry Affine geometry Algebraic geometry Analytic geometry Birational geometry Complex geometry Combinatorial geometry Computational geometry Conformal...

In Euclidean geometry, a kite is a quadrilateral with reflection symmetry across a diagonal. Because of this symmetry, a kite has two equal angles and...

In geometry, a prism is a polyhedron comprising an n-sided polygon base, a second base which is a translated copy (rigidly moved without rotation) of the...

In mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections. Dihedral groups are among the...

these opposites are equal. Coordinate transformation Erlangen program Symmetry (geometry) Motion Reflection Rigid transformation Rotation Topology Transformation...

In theoretical physics, explicit symmetry breaking is the breaking of a symmetry of a theory by terms in its defining equations of motion (most typically...

In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets, or sides, with three meeting at each vertex. Viewed from a...

Polytopes and Symmetry. Cambridge University Press. p. 75. ISBN 9780521277396. Dupuis, Nathan Fellowes (1893). Elements of Synthetic Solid Geometry. Macmillan...

chief alternative to octahedral geometry is a trigonal prismatic geometry, which has symmetry D3h. In this geometry, the six ligands are also equivalent...

In mathematics, integral geometry is the theory of measures on a geometrical space invariant under the symmetry group of that space. In more recent times...

mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate...

It has two lines of reflectional symmetry and rotational symmetry of order 2 (through 180°). In spherical geometry, a spherical rectangle is a figure...

the four known fundamental forces in the universe, may be modelled by symmetry groups. Thus group theory and the closely related representation theory...