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Point reflection

In geometry, a point reflection (also called a point inversion or central inversion) is a geometric transformation of affine space in which every point is reflected across a designated inversion center, which remains fixed. In Euclidean or pseudo-Euclidean spaces, a point reflection is an isometry (preserves distance). In the Euclidean plane, a point…

Standards, Properties & Inversion centers in crystals and molecules

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Overview

Terminology

Examples

Formula

Point reflection as a special case of uniform scaling or homothety

Point reflection group

Point reflections in mathematics

Point reflection in analytic geometry

Properties

Inversion centers in crystals and molecules

Inversion with respect to the origin

Advanced semantic analysis

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Map overview Semantic statistics

Point reflection

Nodes111
Edges110
Triples41
Avg. degree1.98
Density0.018018
Components1

How this topic connects Entity context

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Point reflection

Top relations

related to Inversion with respect to the origin · 7
Point reflection → Cartesian, Euclidean, In, Inversion, Reflection, Rn, The
related to Point reflection group · 6
Point reflection → Euclidean, It, Lie, Rn, Specifically, The
related to Terminology · 6
Point reflection → Euclidean, In, More, Reflection, Such, The
is a · 4
Point reflection → involution, isometry, same as a half-turn rotation, same as a rotation of 180 degrees
related to Formula · 4
Point reflection → Euclidean, Given, In, Rn
related to Point reflections in mathematics · 4
Point reflection → Lie, Point, Riemannian, Symmetric
related to Point reflection as a special case of uniform scaling or homothety · 2
Point reflection → This, When
related to Examples · 1
Point reflection → In

Important terminology Word statistics

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Important terminology

point reflection inversion group center polyhedra origin also space euclidean displaystyle plane orthogonal transformation symmetry identity called geometry rotation centrosymmetric

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Point reflectionis aisometry0.90text
Point reflectionis asame as a half-turn rotation0.90text
Point reflectionis ainvolution0.90text
Point reflectionis asame as a rotation of 180 degrees0.90text
oxides these polyhedra can link together via corner-instance ofIn many materials0.80text
edge- or face sharinginstance ofIn many materials0.80text
depending on which atoms share common bondsinstance ofIn many materials0.80text
also the valenceinstance ofIn many materials0.80text
for metalsinstance ofIn other cases0.80text
alloys the structures are better considered as arrangements of close-packed atomsinstance ofIn other cases0.80text
Jahninstance ofoften due to differing electrostatic interactions between heteroatoms or electronic effects0.80text
Point reflectionrelated to ExamplesIn0.60section

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    Min side: 3
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