To install click the Add extension button. That's it.

The source code for the WIKI 2 extension is being checked by specialists of the Mozilla Foundation, Google, and Apple. You could also do it yourself at any point in time.

Kelly Slayton
Congratulations on this excellent venture… what a great idea!
Alexander Grigorievskiy
I use WIKI 2 every day and almost forgot how the original Wikipedia looks like.
Live Statistics
English Articles
Improved in 24 Hours
Added in 24 Hours
What we do. Every page goes through several hundred of perfecting techniques; in live mode. Quite the same Wikipedia. Just better.

Polar point group

From Wikipedia, the free encyclopedia

In geometry, a polar point group is a point group in which there is more than one point that every symmetry operation leaves unmoved.[1] The unmoved points will constitute a line, a plane, or all of space.

While the simplest point group, C1, leaves all points invariant, most polar point groups will move some, but not all points. To describe the points which are unmoved by the symmetry operations of the point group, we draw a straight line joining two unmoved points. This line is called a polar direction. The electric polarization must be parallel to a polar direction. In polar point groups of high symmetry, the polar direction can be a unique axis of rotation, but if the symmetry operations do not allow any rotation at all, such as mirror symmetry, there can be an infinite number of such axes: in that case the only restriction on the polar direction is that it must be parallel to any mirror planes.

A point group with more than one axis of rotation or with a mirror plane perpendicular to an axis of rotation cannot be polar.

YouTube Encyclopedic

  • 1/3
    36 517
    315 240
    1 824 325
  • Classification of molecules into point group. Part-1 (CHE)
  • Polar and NonPolar Molecules: How To Tell If a Molecule is Polar or Nonpolar
  • Polar & Non-Polar Molecules: Crash Course Chemistry #23


Polar crystallographic point group

Of the 32 crystallographic point groups, 10 are polar:[2]

Polar crystallographic point groups
Crystal system Polar point groups
   Schönflies    Hermann–Mauguin Orbifold Coxeter
Triclinic C1 1 11 [ ]+
Monoclinic C2 Cs 2 m 22 * [2]+ [ ]
Orthorhombic C2v mm2 *22 [2]
Trigonal C3 C3v 3 3m 33 *33 [3]+ [3]
Tetragonal C4 C4v 4 4mm 44 *44 [4]+ [4]
Hexagonal C6 C6v 6 6mm 66 *66 [6]+ [6]
Cubic (none)

The space groups associated with a polar point group do not have a discrete set of possible origin points that are unambiguously determined by symmetry elements.[1]

When materials having a polar point group crystal structure are heated or cooled, they may temporarily generate a voltage called pyroelectricity.

Molecular crystals which have symmetry described by one of the polar space groups may exhibit triboluminescence.[3] A common example of this is sucrose, demonstrated by smashing a wintergreen lifesaver in a darkened room.


  1. ^ a b Jeremy Karl Cockcroft, Huub Driessen, David Moss, Ian Tickle (2006). "Polar Point Groups". University of London. Retrieved 2013-12-09.CS1 maint: uses authors parameter (link)
  2. ^ Kasap, Safa O. (2006). Principles of electronic materials and devices. Boston: McGraw-Hill. ISBN 9780073104645.
  3. ^ Zink, Jeffery (1981). "Triboluminescence-Structure Relations in Polymorphs of Hexaphenylcarbodiphosphorane and Anthranilic Acid, Molecular Crystals, and Salts". J. Am. Chem. Soc. 103: 1074–1079. doi:10.1021/ja00395a014.
This page was last edited on 2 February 2020, at 05:27
Basis of this page is in Wikipedia. Text is available under the CC BY-SA 3.0 Unported License. Non-text media are available under their specified licenses. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc. WIKI 2 is an independent company and has no affiliation with Wikimedia Foundation.