# Difference between revisions of "Symmetry"

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Every crystal belongs to a particular crystal system (cubic, tetragonal, hexagonal, trigonal, orthorhombic, monoclinic or triclinic) and the symmetry for each of these systems is defined by ideal shapes. | Every crystal belongs to a particular crystal system (cubic, tetragonal, hexagonal, trigonal, orthorhombic, monoclinic or triclinic) and the symmetry for each of these systems is defined by ideal shapes. | ||

− | Following is an illustration of symmetry axes in the orthorhobic system. | + | Following is an illustration of symmetry axes in the orthorhobic system.<br /> |

+ | When determining the axes symmetry it is important to rotate (or spin) the crystal around that axis through a 360° rotation and judge how many times the exact image is repeated during the rotation. | ||

[[image:Orthorhombic-matchbox-side.jpg|thumb|200px|left|The basic form that makes up the orthorhombic system looks like a matchbox]] | [[image:Orthorhombic-matchbox-side.jpg|thumb|200px|left|The basic form that makes up the orthorhombic system looks like a matchbox]] | ||

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[[Image:Orthorhombic9.jpg|thumb|200px|left|We now take a pinacoidal face (the front plane) as the start of our rotation]] | [[Image:Orthorhombic9.jpg|thumb|200px|left|We now take a pinacoidal face (the front plane) as the start of our rotation]] | ||

[[Image:Orthorhombic10.jpg|thumb|200px|left|And again, during a 360° rotation of the prism around the axis, the exact same image is shown twice]] | [[Image:Orthorhombic10.jpg|thumb|200px|left|And again, during a 360° rotation of the prism around the axis, the exact same image is shown twice]] | ||

− | [[Image:Orthorhombic-matchbox.jpg|thumb|200px|left|If one would place the matchbox on one of the pinacoidal faces, one would get identical results]] | + | [[Image:Orthorhombic-matchbox.jpg|thumb|200px|left|If one would place the matchbox on one of the pinacoidal faces, one would get identical results]] <br clear="all" /> |

+ | |||

+ | As can be seen in the above images there are 3 axes of symmetry in the orthorhombic system and each axis produces the same image twice during a 360° spin around that axis.<br /> | ||

+ | When an axis shows the same image twice, we name it a 2-fold axis of symmetry (or better: a "digonal axis of symmetry"). So the orthorhombic system is characterized by 3 2-fold axes of symmetry. | ||

+ | |||

+ | Other crustal systems will have less or more axes of symmetry. A 3-fold axis of symmetry means that the image is repeated 3 times (named a "trigonal axis of symmetry") etc. | ||

+ | |||

+ | ===Planes of symmetry=== | ||

+ | |||

+ | ===Center of symmetry=== | ||

+ | |||

+ | ===Sources=== | ||

+ | |||

+ | * [http://yey.be/orthorhombic.html Symmetry made easy] |

## Revision as of 08:36, 19 November 2006

This section is currently under construction, do not edit until this message is gone | |

--Doos 06:10, 19 November 2006 (PST) |

## Basic

### Axes of symmetry

Axes of symmetry have to do with balance of shape when rotated around these imaginary axes.

Every crystal belongs to a particular crystal system (cubic, tetragonal, hexagonal, trigonal, orthorhombic, monoclinic or triclinic) and the symmetry for each of these systems is defined by ideal shapes.

Following is an illustration of symmetry axes in the orthorhobic system.

When determining the axes symmetry it is important to rotate (or spin) the crystal around that axis through a 360° rotation and judge how many times the exact image is repeated during the rotation.

As can be seen in the above images there are 3 axes of symmetry in the orthorhombic system and each axis produces the same image twice during a 360° spin around that axis.

When an axis shows the same image twice, we name it a 2-fold axis of symmetry (or better: a "digonal axis of symmetry"). So the orthorhombic system is characterized by 3 2-fold axes of symmetry.

Other crustal systems will have less or more axes of symmetry. A 3-fold axis of symmetry means that the image is repeated 3 times (named a "trigonal axis of symmetry") etc.