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Topic: Point groups

Related Topics

Crystallographic point group

Symmetry group

3D crystallographic group

Space group

Crystallographic group

Group (mathematics)

Group theory

Symmetric group

Crystal system

Symmetry

Crystal structure

Monoclinic

Cubic (crystal system)

Rhombohedral

Triclinic

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	Point groups in three dimensions - Wikipedia, the free encyclopedia
		In geometry a point group in 3D 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 which leave the origin fixed, or correspondingly, the group of orthogonal matrices.
		, and is the symmetry group of the cube and octahedron.
	en.wikipedia.org /wiki/Point_groups_in_three_dimensions (3402 words)

	Point group - Wikipedia, the free encyclopedia
		In mathematics, a point group is a group of geometric symmetries (isometries) leaving a point fixed.
		A discrete point group in 2D is sometimes called a rosette group, and is used to describe the symmetries of an ornament.
		The 3D point groups are heavily used in chemistry, especially to describe the symmetries of a molecule and of orbitals forming covalent bonds, and in this context they are also called molecular point groups.
	en.wikipedia.org /wiki/Point_group (453 words)

	PlanetMath: examples of groups
		This is the automorphism group of the given object and captures its “internal symmetries”.
		In Galois theory, the symmetry groups of field extensions (or equivalently: the symmetry groups of solutions to polynomial equations) are the central object of study; they are called Galois groups.
		All these matrix groups are Lie groups: groups which are differentiable manifolds such that the group operations are smooth maps.
	planetmath.org /encyclopedia/ExamplesOfGroups.html (1011 words)

	Encyclopedia :: encyclopedia : Point groups in three dimensions (Site not responding. Last check: 2007-11-03)
		The rotation group of an object is equal to its full symmetry group iff the object is chiral.
		In the case of multiple mirror planes and/or axes of rotation, two symmetry groups or of the same symmetry type iff there is a single rotation mapping this whole structure of the first symmetry group to that of the second.
		We restrict ourselves to isometry groups where for all points the set of images under the isometries is topologically closed.
	www.hallencyclopedia.com /topic/Point_groups_in_three_dimensions.html (3420 words)

	Use of Point Groups
		All molecules in D point groups all have multiple C axes and therefore cannot be polar.
		One of the most practical uses of point groups and group theory for the inorganic chemist in is predicting the number of infrared and Raman bands that may be expected from a molecule.
		It is still pointed along the z-axis, but it does change in magnitude (increasing with the bend).
	www.reciprocalnet.org /edumodules/symmetry/pointgroups/use.html (919 words)

	[No title]
		In the crystallographic group p1, all the symmetries are translations and the point group is trivial.
		Horizontal arrows between two groups denotes the minimal index in which the group on the left lies as a proper subgroup in the group on the right and vice versa.
		The groups p3m1 and p31m have two lines connecting them since p3m1 is a normal subgroup of index 3 in p31m while p31m is a subgroup of index 3 in p3m1 but it is not a normal subgroup.
	members.tripod.com /vismath8/tennant/index.html (1143 words)

	Symmetry Groups
		This has been a primary motivation for developing the branch of mathematics known as "group theory." There are many kinds of symmetry, but the symmetries of rigid bodies are the most important and useful, because they are the most ubiquitous as well as the most obvious.
		Each of the 32 lattice point groups and 230 space groups in three dimensions is generated from a set of three symmetry vectors.
		Euclidean points are given a homogeneous representation that avoids designating one of them as an origin of coordinates and enables direct computation of geometric relations.
	modelingnts.la.asu.edu /html/SymmetryGroups.html (365 words)

	The point groups
		It often seems that the point group associated with the symmetry group of a pattern is the group of symmetries of the motif and that the point group is then a subgroup of the group of symmetries.
		In this case the symmetry group of the motif and the subgroup fixing a point of the lattice are both trivial and so are not the same as the point group.
		The point group is not a subgroup of the symmetry group.
	www-groups.dcs.st-and.ac.uk /~john/geometry/Lectures/A3.html (449 words)

	Fund-Raising Programs, Jobs, Cedar Point (Site not responding. Last check: 2007-11-03)
		Group members will be expected to stand for long period of time and working in all weather conditions during the cold fall weekends.
		At the assigned locations, the group may have a variety of responsibilities including, but not limited to: food sales, cash handling, cleaning, stocking, clearing tables, food preparation, greeting guests, washing dishes, rolling silverware, providing excellent guest services, etc. Location assignments are subject to change at the discretion of the division at anytime.
		Group members will be expected to stand for long periods of time and to work in all types of weather conditions, including extreme hot/cold temperatures.
	www.cedarpoint.com /public/jobs/fund_raising.cfm (1313 words)

	[No title]
		Thus, the symmetry of the atoms in the unit cell is reflected in the intensities of the diffraction pattern.
		Laue symmetry can be, at least approximately, described by one of the 11 centrosymmetric point groups that result from adding a center of symmetry to each of the 32 crystallographic point groups.
		Associated with each point group is a ‘character table’ which contains information needed to work out all of the properties that depend on the molecular symmetry.
	www.lycos.com /info/symmetry--point-groups.html (236 words)

	Three-Dimensional Space Groups
		By combining the permissible point groups with their possible lattices, we find 11 of the 17 plane space groups.
		Groups cannot have a lattice with lower symmetry than that of the space group.
		There are a total of 73 space groups that arise from repeating a motif with one of the point group symmetries according to the possible Bravais Lattices.
	www.uwgb.edu /dutchs/SYMMETRY/3dSpaceGrps/3DSPGRP.HTM (623 words)

	Chapter 1.3
		As the basis for the classification of the symmetry groups G three elements were taken into consideration: the types of symmetries (isometries, similarity symmetries, conformal symmetries) that occur in G, the space on which the group G acts, and the sequence of maximal included proper subspaces, invariant with respect to the group G.
		A lattice is the orbit of a point with respect to a discrete group of translations.
		In isometry groups all distances between points under the effect of symmetries remain unchanged and the congruence of homologous figures is preserved.
	www.emis.de /monographs/jablan/chap13.htm (2381 words)

	Development:Groups documentation for module developers - MoodleDocs
		The main changes is that there may be a different set of groups being used for each instance of you module in the course and that separate/visible groups have been replaced by a better system of permissions.
		From a student's point of view, groups are generally used as a way to enable parallel versions of the same activity with different groups of students e.g you might want a separate forum or wiki for each group.
		Then when displaying calendar entries to users, need to know which groups a particular has view permission for across all courses though it's a tiny bit more complicated that this because a grouping can be used for more than one course and someone may be a student on one course and a teacher on another.
	docs.moodle.org /en/Groups_documentation_for_module_developers (1832 words)

	Group Theory
		Group Theory is one of the most powerful mathematical tools used in Quantum Chemistry and Spectroscopy.
		Each of these Symmetry Operations is associated with a Symmetry Element which is a point, a line, or a plane about which the operation is performed such that the molecule's orientation and position before and after the operation are indistinguishable.
		The key to applying Group Theory is to be able to identify the "Point Group" of the molecule i.e.
	www.science.siu.edu /chemistry/tyrrell/group_theory/sym1.html (487 words)

	Lecture 2: Point Symmetry in 2- and 3-D
		Every crystal has one of these 32 point groups as its underlying structure - if the crystal is able to form unhindered, its outward morphology (shape) should be identifiable as belonging to one of these 32 classes.
		These 32 point groups are also known as the 32 crystal classes which have been grouped in Table 2.2 into 6 crystal systems based on the major or special rotational rotation axis.
		In the 3rd lecture we completed the overview of three dimensional point symmetries by covering rotoinversion, combinations of rotations and the addition of perpendicular mirrors to many of the preceeding point groups.
	www.geology.wisc.edu /courses/g360/lect2.html (1371 words)

	Crystallographic Topology - Cubic Groups
		The 36 cubic crystallographic space groups are different from the remaining 194 space groups in that they each have body diagonal 3-fold axes arising from their tetrahedral and octahedral point groups.
		The seven rhombohedral trigonal subgroups of the cubic groups are shown in the bottom row of the figure with their space group symbols and simplest lattice complex in the top row of each box.
		The divider strip between the cubic and rhombohedral groups gives the point groups for all the groups involved in each column, with the cubic/orthorhombic (or tetragonal) to the left and the rhombohedral/monoclinic (or triclinic) to the right.
	www.ornl.gov /sci/ortep/topology/cubicgsg.html (1827 words)

	Grace Point Church Las Vegas
		Grace Point Groups are smaller environments created to help you explore relevant life issues from a biblical perspective.
		Groups meet in homes throughout the north part of Las Vegas at various times throughout the week.
		Grace Point Groups are on a break during the month of December.
	www.gracepointvegas.com /gpgroups (166 words)

	Point Groups
		Point groups are a method of classifying the shapes of molecules according to their symmetry elements.
		The inversion center (or point of symmetry) is an imaginary point in a compound.
		point group at short time scales, when it is in a single chair form, but at longer time scales, at which it is in rapid equilibrium between its two chair forms, it is in the D
	www.chem.uky.edu /research/Grossman/stereo/pointgroups.HTML (692 words)

	North Point Community Church: General FAQ
		These groups consist of six to eight individuals or five to six couples who meet regularly for Bible study and prayer and commit to accountability, friendship, and support.
		By participating in small groups outside of the regular Sunday morning schedule, adults are free to serve in a ministry area on Sunday mornings.
		The purpose of this group is to determine programming, give vision to the various ministries of the church, and oversee the day-to-day operations.
	www.northpoint.org /faq-general (1092 words)

	Turning Point Ministries
		With its emphasis on developing Christian character it is a powerful group for those who want to be sure to prevent life-controlling problems from developing in their lives, as well as for those who need to overcome a current problem.
		Written by a pediatrician, this group study is full of information on the physical, spiritual, and emotional needs of children in every state of development, and explores strategies to be the parent God has called you to be.
		This group is a couples only group for those who may be experiencing difficulties in their marriage.
	www.lhc-arts.org /lhc/turning_point.html (1174 words)

	Introduction to Space Groups (Site not responding. Last check: 2007-11-03)
		The point group symmetry operations applied to a motif can be deduced from the external symmetry of a (perfect) crystal.
		A combination of the point group symmetry operations leads to 32 point groups.
		Thus these symmetry elements involving translations are also referred to as internal symmetry elements, in contrast to the externally observable point group operations (point groups or Crystal Classes).
	www.ruppweb.org /xray/tutorial/spcgrp_tut.htm (860 words)

	[No title] (Site not responding. Last check: 2007-11-03)
		The dots you see moving around are generated by the selected point group (a set of rotational symmetry operations).
		Each dot is the projection of a plane normal (that intersects the stereographic hemisphere) onto the equator plane (represented by the Wulff net) A solid dot represents a normal pointing out of the screen, and an empty circle represents one pointing away from you.
		Be aware that the calculation of general icosahedral polyhedra with 60 or 120 planes in the point groups 235 and m-3-5 may take quite a while even on fast computers.
	jcrystal.com /steffenweber/JAVA/jpoly/jpoly.html (262 words)

	Categorisation of point groups
		This table lists point group symmetries along with their symmetry operations, the order of the group (i.e.
		This, in the case of crystolographic point groups, is the Laue class which corresponds to the symmetry of reciprocal space.
		Isomorphic groups are also listed where character tables are available.
	newton.ex.ac.uk /research/qsystems/people/goss/symmetry/CC_All.html (129 words)

	The Point Groups.
		We may name the points in some arbitrary order and write down this as (1,2,3,..,n) for a collection of n points.
		The points that are exchanged are of cource those at the coordinates x and -x relative to each other.
		a combination of a rotation and an inversion is that the set of points may not be coincident after the rotation.
	hemsidor.torget.se /users/m/mauritz/math/alg/symop.htm (782 words)

	Point Groups
		The idea behind this script is to visualise the different point groups by drawing representative crystal cells and also visualising the possible symmetry operations for each.
		It is hoped that this will help people new to the subject to understand what point groups are all about.
		It elaborates on a description of point groups using Geometric Algebra that was developed by David Hestenes.
	www.perwass.de /CLU/html/point_groups.html (104 words)

	III: Other point groups (Site not responding. Last check: 2007-11-03)
		There are nine equivalence classes corresponding to the cases where the point group is D
		In all these cases the point group is generated two reflections R
		We will find that there are 9 possible combinations of point groups and shift vectors.
	www-groups.dcs.st-and.ac.uk /~john/geometry/Lectures/A8.html (320 words)

	Point of Action (Site not responding. Last check: 2007-11-03)
		Point of Action LLC is a full-service training consulting company that delivers ongoing corporate training planning, as well as practical training workshops, for local and regional accounting and financial advisory firms.
		Point of Action's philosophy and methodology focus on Practical Business Learning - delivering relevant, high-impact training services for your organization - which leads to higher productivity, increased client satisfaction, and improved profitability.
		Point of Action provides four primary consulting services that will improve the quality and impact of your staff training programs.
	www.pointofaction.net (133 words)

	8.10.1 Representation of Point Groups (Site not responding. Last check: 2007-11-03)
		The 57 groups recognized in MOPAC are given in Table 8.38.
		Each point group is represented by a subset of the associated point-group table.
		Although it is not obvious, all 120 operations of the group can be generated as products of these four operations.
	home.att.net /~mopacmanual/node562.html (161 words)

	Automatic Point Groups
		Select a point and list the groups it belongs to, then add it to any number of existing groups.
		AutoGroups actually shows you a list of unique point descriptions and lets you click to add them along with a group (or groups) name you select or enter to create associations of descriptions and groups.
		Drawing points MUST be in the drawing when the program is run.
	www.budcad.com /AutoGroups.htm (472 words)

	High Point Museum
		The High Point Museum is the only place to learn, play and explore the real history of High Point.
		The High Point Museum was selected as a winner of the 2006 American Association of Museums Publications Design Competition.
		Focus groups helped the museum identify sections of history to expand and helped the museum collect artifacts to put on display.
	www.highpointmuseum.org (201 words)

	Three-Dimensional Point Groups
		For more information on the 32 crystallographic point groups, see Crystallographic Point Groups.
		Rotoinversion requires rotating a point by 360/n degrees, then inverting it through the center as shown in the upper left.
		If n is even and divisible by 4, there are n points alternating up and down.
	www.uwgb.edu /dutchs/symmetry/3dptgrp.htm (900 words)

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