I don't know of any concrete examples of "tritwise tricks" (this is not my area of expertise). But as ternary logic is a superset of boolean logic there are more possibilities available (3*3=9 different state transitions compared to 2*2=4) and some of them are bound to be useful. For example it should be possible to represent combinations of two bitwise operations as an equivalent tritwise operation (eg. x XOR A OR B where A and B are constants in binary could become x "XOROR" C in ternary) – but that feels like an example constructed by someone who is still thinking in binary. I'm certain that someone much smarter than me could come up with ternary-native data types and algorithms.
If ternary logic has not been widely studied I assume there is a lot to be discovered still.
If ternary logic has not been widely studied I assume there is a lot to be discovered still.