4D, I was taught that the 4- basic dimensions are: X, Y, Z & Time, do you concur?
I like the way you think and solve problems. You also have a tremendous gift of self-critique to improve on your initial designs.
Otis Guillebeau (inventor) from Auburn, Georgia
As for dimensions it depends on who you ask. I had a college studio professor who balked at me when I claimed my project for him had a 4th dimension (of time). The office space I designed (a 1st floor bank in a multi-floored building) could be reconfigured during the evening non-business hours to keep upper floor visitors and tenants out of the bank spaces, but permit easy access to banking resources during banking hours. He eventually accepted my 4th.
On a CNC we may have X,Y,Z and A (rotary) for 4, as well as X,Y,Z,A and B for 5 where A and B are two more dynamic dimensions of bit movement/orientation during a cut. You could consider the variety of router bits used a unique dimension. Change the bit and you change the outcome.
String theorists might insist there are 10, 11, or 26 dimensions.
I try and stick to 4 where time is the 4th. Of my own designs many have more than one configuration their 3 dimensions can change to or through. A chair that folds up for flat storage has a 4th dimension. It can't be folded AND unfolded at the same moment, so each state exists at different times. A coffee table of 4 parts that can be re-arranged to change the height of the top has a 4th dimension. A tv-tray stand that can turn inside out to present a flat or a sloped top (for tablet/laptop use) has a 4th dimension. Etc..
The open frame design of Probotix' CNCs permits re-configuring it for complex cuts as your needs change over time. Keeping the 3 axis of movement the same, but adding new orientations for clamping work beneath them lets one take advantage of their 4th dimension potential.