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A library of common geometric shapes can be used to train our brains for understanding data structure in high-dimensional Euclidean space. This article describes the methods for producing cubes, spheres, simplexes, and tori in multiple dimensions. It also describes new ways to define and generate high-dimensional tori. The algorithms are described, critical code chunks are given, and a large collection of generated data are provided. These are available in the R package geozoo, and selected movies and images, are available on the GeoZoo web site

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