Can any mathematician give me an algorithm that scales up to

>>9129624
Something that can be programmed on computer

Here's what I have going so far. If anybody can help I would appreciate or is this enough to solve for all the unknown already. I just haven't completely tried it out yet.

There are several restrictions we can use in a system of equations to arrive at the rotation. First, the distance of the moved point or any point of rotation has a distance from the origin of rotation the same as the starting point. The distance to the end point of the axis of rotation vector is also maintained, as are any number of points between the end point and the origin of rotation, which if I'm not mistaken give an endless number of additional restrictions, but one more is essential. The total distance between two points in a rotation approaches radians * radius / 2 pi, and so we can break that down to an infinitesimal and add those up because of circumference equation.

Another method I was thinking of involved using slices with an upgraded polytope in a higher dimension to make up the hypersurface where a rotation could be done using spherical coordinates along each expansion of dimensions following a single path of polytope neighbours.

>>9129624
>axis

You mean plane-angle rotation. For plane in the i-th and j-th dimension, it's just the identity matrix were eii and ejj are removed and replaced by cos(angle)*eii + cos(angle)*ejj -
sin(angle)*eij + sin(angle)*eji

>>9129624
In N dimensions, you are rotating around an (N-2)-plane.

Just look at rotation matricies.
They are a subset of orthonormal matricies (transpose is equivalent to inverse)
Note: some orthonormal transformations will flip the directions of some of your axes.

Basically, if your plane of rotation doesn't pass through the origin, perform a shift to make it so, then do the rotation, then shift it back.