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The cube is such a familiar object that few people know its formal name: the regular hexahedron. Yet that familiarity is deceptive... To see why, let’s slice a cube into sections: this old familiar shape still has a few surprises in store!
Discrete geometry is a recent field of research concerned with "discrete objects," such as graphs and tilings. But it also offers a fresh perspective on problems that are difficult to solve in a continuous setting, including the existence of regular polygons with integer-coordinate vertices.
