Template:Symmetry

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.