This is a Klein bottle that has been mapped onto the surface of a hypersphere.
Well...not really. It can't be done. (The topological explaination is, since Klein bottles are not ΓÇ£orientableΓÇ¥ they can't exist in any orientable three dimensional space, and the surface of a hypersphere is three dimensional.) This particular Klein bottle intersects itself.
It can be made by gluing two Mobius strips together at their edges. (See the Mobius Strip files.)
This particular Klein bottle was made from two Mobius strip grids that were 16 squares long and 4 squares wide. You could consider it a single grid that was 16 by 8.
It was mapped onto a hypersphere with the formula:
Given a rectangular patch [a,b] where 0┬░ΓëñaΓëñ360┬░, and -90┬░ΓëñbΓëñ90┬░, map [a,b] onto [x,y,z,t] with:
x = cos(a) cos(b)
y = sin(a) cos(b)
z = cos(2a) sin(b)
t = sin(2a) sin(b)
The seam where the two Mobius strips meet is at b=0, in the xy plane.
