Mike,
I believe these free scripts should work for CC:
s.h's page : Scripts for Adobe Illustrator CS
If they do, you may try to apply the Divide (length) script to both the circle and the triangle, setting the number (of added Anchor Points to each segment) to 3 for the triangle and to 2 for the circle. This should give 12 sets of corresponding Anchor Points on the two paths and thereby nice blends (either way).
This will also work similarly for whichever polygons you may choose.
Or for this case, you can use Object>Path>Add Anchor Points twice on the triangle to get the 3 added Anchor Points in each segment to give the total of 12 segments, and use a Polar Grid instead of the circle with the following extension:
1) Create the Polar Grid with the desired radius/diameter, set Concentric Dividers to 0 and set Radial Dividers to 12;
2) Deselect and Select the Radial Divider Group within the Polar Grid Group (you can do it in the (expanded) Layers palette), then tick the centre Reference Point in the Transform palette and multiply the W or H value by 1.2 (or something like that) and press Ctrl/Cmd+Enter; this will make them stick out past the circle;
3) Select the whole Polar Grid Group and Pathfinder>Divide, then Ctrl/Cmd+Shift+G to Ungroup and Ctrl/Cmd+J to Join; this will give the total of 12 segments;
The reason for the radial divider extension is the inherent bulging of a Bezier circle.
There are other similarly silly ways to obtain the desired divisions for many other combinations, but they will most likely have to be customized.