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A tesseract or hypercube is

A tesseract or hypercube is a piece of hypothetical four-dimensional geometry that is generated by dragging a cube across a fourth dimension much as that cube is generated by dragging a square across three dimentional space. There’s a fair amount on the net about them, but my favourite site (simply called Tesseract) includes a projection of the 4-d hypercube onto three dimensions. It’s not entirely clear from the simulation how or what such an entity operates. But for more about this, and other geometric/dimensional wonders, you can’t go far wrong with Flatland.