see, you cant ignore the rest of the puzzle, because they are required for movement on the order-4 minx.

But, mechanically speaking, they are different. order-4 minx center pieces would join at the center, like a 4x4x4 cube.
A dogic, the piece join halfway between the outer and inner parts.

The order-4 minx centers move exactly like the dogic centers, except for the fact that they MUST be turned with teh puzzle, it is impossible to ignore that fact

I think it's like this:
On an order 4 megaminx (see picture of face posted earlier in thread), if you remove/ignore the edge pieces, you are left with exactly the same puzzle as the dogic.

The megaminx face centres correspond the the dogic tips (you can turn a single layer which moves 5 of them around, or a double layer which also moves 2 from each adjacent face).
The megaminx corners correspond the the dogic centres (they are three-coloured, adjacent to three of the other pieces)

On an order 5 megaminx, the dogic pieces correspond to the corners and the nearest face centre pieces (not the face centre pieces adjacent to the middle edge pieces)

J

The num,ber of positions would be about 10^166. not as much as the masterminx...

For a puzzle to be an order 4 megaminx, it is necessary for the centre pieces not to be independent of the corners. So it is not a dogic.

THe dogic centers would be "invisible" pieces, like the theoretical 2x2x2 hidden inside of a 4x4x4. The centers corespond to the interior 2nd orter megaminx (impossiball) and the tips coraspond to the centers of the 4th order megaminx, the rest of the pieces on a 4th order megaminx simply aren't there, so nothing corasponds to its outer corners or edges

Wow!