Is it possible to construct a four-dimensional hypersphere where every point on the surface is equidistant from the center, yet with all three of the surface dimension being orthogonal to each other and the radius? Also, the radius is some finite value and -- according the data I'm trying to interpret -- the size of the circumference of the sphere appears to be a function of the radius. That is, is it possible to construct a four-dimensional hypersphere with a curvature of 0? If so, what would you call it?
It would be just like one dimension down. A plane is in a sense the limit of a sphere as the radius runs off to infinity. The two axes in the plane are perpendicular to the radius. If you accept this as a construction, it works. In four dimensions you would have a three space that works the same way, being a limit of a hypersphere as the radius goes to infinity. That is useful for some purposes, but you need to be careful to justify the construction in your use.