Polytopes & Tesseract
“Polytopes” is the generic term for geometric objects with flat surfaces, while the specific 2D, 3D, and 4D specific terms are the following:
- 2D: Polygon, e.g. Square
- 3D: Polyhedron, e.g. Cube (hexahedron)
- 4D: Polychoron, e.g. Tesseract or 4D-Hypercube, or 4-cube
On an early pictorial representation of 4D, from “The fourth dimension” (1912), by George Hinton, p. 286:
Tesseract coloring, by Howard Hinton
Vision of the Tesseract, by Piotr Kowalsky:
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