As a field expert in higher-dimensional geometry, I can tell you that a four-dimensional cube is commonly referred to as a tesseract. It's a polytope that extends the concept of a cube into the fourth dimension. A tesseract is also known as an 8-cell or a hexachoron.

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In geometry, the tesseract is the four-dimensional analog of the cube; the tesseract is to the cube as the cube is to the square. Just as the surface of the cube consists of six square faces, the hypersurface of the tesseract consists of eight cubical cells. The tesseract is one of the six convex regular 4-polytopes.read more >>