Left-Right
Most machines are in a Left-Right Doublet.
Machines only with rotations around the Base's Left-right Axis are automatically Left-Right Singlets.
Of machines with rotations that aren't around the Left-right Axis, the I Infinity is the simplest Left-Right Singlet:
A classic machine that is a Left-Right Singlet is the Naked Singularity.
I like creating this type of machine, and did so early in some mashup machines, like the Boo-lemoi and the Barrel Ninja.
I have a set of "Singularity" machines, including the Dressed Singularity (which isn't quite the Reverse of the Naked Singularity):
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