Four-dimensional space (4D) is the mathematical extension of the concept of three-dimensional space (3D). Three-dimensional space is the simplest possible abstraction of the observation that one needs only three numbers, called dimensions, to describe the sizes or locations of objects in the everyday world.
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The mathematical objects that live on the sphere in four dimensional space -- the hypersphere -- are both beautiful and interesting. The four dimensional sphere is a unique object, with properties both similar to and surprisingly different from those of our ordinary sphere. Similarly to the case in three dimensions, there is a family of Platonic and Archimedean solids that can be viewed on the ...