# Template:Symmetry

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This is a template for including symmetry categories for patterns.

For example,

`{{Symmetry|orthogonal4|osc=flip}}`

adds the categories Category:Patterns with rectangular orthogonal symmetry and Category:Flipping oscillators to the page. Typing

`{{Symmetry|180degree}}`

adds only Category:Patterns with 180-degree rotation symmetry, whereas

`{{Symmetry|osc=turn90}}`

adds only Category:Non-flipping oscillators that turn 90 degrees.

Options are

`orthogonal2`: Patterns with reflection symmetry in exactly one orthogonal axis (Category:Patterns with bilateral orthogonal symmetry).`orthogonal4`: Patterns with reflection symmetry in both orthogonal axes (Category:Patterns with rectangular orthogonal symmetry).`diagonal2`: Patterns with reflection symmetry in exactly one diagonal axis (Category:Patterns with bilateral diagonal symmetry).`diagonal4`: Patterns with reflection symmetry in both diagonal axes (Category:Patterns with rectangular diagonal symmetry).`180degree`: Patterns with 180-degree rotation symmetry (Category:Patterns with 180-degree rotation symmetry).`90degree`: Patterns with 90-degree rotation symmetry (Category:Patterns with 90-degree rotation symmetry).`full`: Patterns with all rotation and reflection symmetry (Category:Patterns with complete square symmetry).

`osc=flip`: Oscillators that flip (reflect) during evolution (Category:Flipping oscillators).`osc=turn180`: Oscillators that rotate 180 degrees during evolution (Category:Non-flipping oscillators that turn 180 degrees).`osc=turn90`: Oscillators that rotate 90 degrees during evolution (Category:Non-flipping oscillators that turn 90 degrees).

This template should not be used if the pattern has no symmetry of any kind.