Four-Dimensional Geometry -- from Wolfram MathWorld

Four-dimensional geometry is Euclidean geometry extended into one additional dimension. The prefix "hyper-" is usually used to refer to the four- (and higher-) dimensional analogs of three-dimensional objects, e.g., hypercube, hyperplane, hypersphere. n-dimensional polyhedra are called polytopes. The four-dimensional cases of general n-dimensional objects are often given special names, such as those summarized in the following table. 2-D 3-D 4-D general circle sphere glome...