I think the "inaccuracies" are from the process/definition of the prims...
a ring18 connects a cyl scaled x18 with one scaled x19, which means the rounding imperfections from the cyl prims get amplified.
(I dont know exactly but it fits: edge/cyl prims have 0.9239 0 0.3827 for the 22.5° position, this multiplied with 19 results in your 17.5541 0 7.2713 values)
a ring18 connects a cyl scaled x18 with one scaled x19, which means the rounding imperfections from the cyl prims get amplified.
(I dont know exactly but it fits: edge/cyl prims have 0.9239 0 0.3827 for the 22.5° position, this multiplied with 19 results in your 17.5541 0 7.2713 values)