Shaped Objects Positioned in a Reference Frame

If I have a shaped object (not a point) in a fixed 3-dim reference frame, I believe it takes 6 "pieces of information" to position it: X, Y, Z, and three orientation angles. If I add another shaped object to the reference frame and want to describe its position relative to the first object, I believe it should take 6 more pieces of information to accomplish this: deltaX, deltaY, deltaZ, and three delta angles for orientation. Each new object added increases the "system information" by 6. Am I thinking about this correctly and can you point me to where I can learn more about this topic?