The Rule of Crayons

Ask a 4 year old to draw the outline of a shape, and "close it". They can do it. They get the concept of a line that connects to itself as "closed". That shape can be an engine cycle. Now they either drew it clockwise or counterclockwise. Ask them to draw it the opposite direction. They can do it. That shape can also be an engine cycle. And since its the same shape, it was "reversed". This is the rule of crayons. Even math professors know it. Any closed path an be traveled in either direction. (Thermo physicists clearly need some 4 year old assistants. :)

An engine cycle is just a closed curve of Pressure versus Volume. To go left and right on volume, your engine volume expands and contracts (usually by compression). To go up and down on pressure, your engine adds or subtracts heat.

The Carnot Cycle is no different. Other than the two Insulated Work Curves, it has two other curve segments which add and subtract heat. They do it while changing volumes, which is in no way unique or even helpful. The cycle is in part a result of a misconception of something called "materiality of heat". (An Automobile engine cycle is much superior cycle to a Carnot Cycle, because it has a greater work ratio for the same total expansion.) One can observe the cycle is very similar to a steam cycle, that was in use in Carnot's time, because the heating model of constant heat is an external combustion model fitting a fire under a boiler. The need to recondense the steam supported the idea that one must "pour" the heat back out.

Any currently manufactured engine cycle is a "single volume" engine cycle. Even if the engine has 8 cylinders, each engine cycle involves only one volume, independent of the other volumes.