Some of the mystery is solved. Here's what I get for the Hip rafter side cut angles expressed as "over 12" values. The 12" is measured along the long axis (length) of the rafter. The angles are laid out on the upper shoulders of unbacked Hip rafters.

At the peak where the Hip rafters meet one another:
4 15/16 over 12
Hip rafter feet intersect plumb planes at the eave lines:
28 7/8 over 12

I'm still having a hard time reconciling the "16" given for the Hip side cut in the original post with any integral base: 12, 16 or otherwise. And perhaps the definition of a "hip side cut angle" in the octogon table is different than that normally given on a framing square. ???
Yeah, a picture or some more information would be nice ... while I still have all my hair. confused

PS: I haven't as yet checked out the file Curtis mentioned in his post; that will likely lend some insight as to what's going on.

Hip-Valley Roof Framing and Joinery Math