A generalization of the cube to dimensions greater than three is called a "hypercube", "n-cube" or "measure polytope". The tesseract is the four-dimensional hypercube, or 4-cube.
According to the Oxford English Dictionary, the word tesseract was coined and first used in 1888 by Charles Howard Hinton in his book A New Era of Thought, from the Greek τέσσερεις ακτίνες, referring to the four lines from each vertex to other vertices. In this publication, as well as some of Hinton's later work, the word was occasionally spelled "tessaract." Some people have called the same figure a tetracube, and also simply a hypercube.
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