Symmetries

Symmetries are sets of translations that transform your diagrams into other shapes. Symmetries can be any combination of x, y and z in order. eg: xz eg: xyz eg: y

A symmetry includes all possible variations of its axes. For example, xy includes all possible variations of x and y . They could flip over, swap around, etc...

Note: When using the xyz symmetry, you must choose a subset (see below).

Subsets

You can also use certain subsets of symmetries. Symmetries have these properties, which let you access subsets:

• directions (only points your diagram in different directions - does not rotate)

• rotations (only rotates your diagram - does not reflect)

• shifts (only points your diagram in different directions and then rotates around those directions - does not do any other rotations or reflections)

• swaps (only swaps the axes with each other)

For example, this element would move in a random xyz direction (6 possible directions):

any(xyz.directions) @_ => _@

This would have 12 transformations:

any(xyz.shifts) {
    @  => _
     _     @
}