15x12? I honestly don't know.
I DO know they made 15x10.5 in small pattern, I have a pair (7.5 bs, front half of a 15x8, back half of a 15x14)
I also have a pair of 15x8.5 sbp, and a pair of 15x5 sbp.
You CAN have the sbp double drilled for a different pattern. My two large pair both have been double drilled.
And you can tell exactly the width of the rim with a tire on it (Assuming it's not marked on the inside)
Inflate the tire (all the following are hypothetical numbers)lay it flat.
Straightedge across the tire section, measure to the ground thru the center hole. 18 inches. Now measure to the rim. 1.5 inches (will be the same on the bottom ) 1.5 times two, subtracted from section, equals 15. Subtract 1/2 twice for bead thickness, equals 14", so 15x14 wheel. Your results will vary.
Technique works on any wheel/mounted tire combo. Just assume a steel rim bead will be less than an aluminum one.