Polychoron

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Complete graph K5.svg
4-simplex
(5-cell)
Cross graph 4.svg
4-orthoplex
(16-cell)
Hypercubestar.svg
4-cube
(Tesseract)
24-cell graph ortho.png
24-cell
120-cell petrie polygon.svg
120-cell
600-cell petrie polygon.svg
600-cell
Graphs of six convex regular 4-polytope.
The tesseract is the best known polychoron, containing eight cubic cells, three around each edge.It is viewed here as a Schlegel diagram projection into 3-space, distorting the regularity, but keeping its topological continuity. The eighth cell projects into the volume of space exterior to the boundary.

In geometry, a polychoron (plural: polychora) is a figure in four dimensions. The word comes from Greek poly, which means many and choros which means room, or space. Sometimes the figure is called 4-polytope or polyhedroid. The analogue figure in two dimensions is a polygon, and the one in three dimensions is a polyhedron.


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