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J34
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The 600-Cell
The 600-cell is a four-dimensional, convex, regular polytope. Its dual is the 120-cell, also known as the hyperdodecahedron. Since the dual of the dodecahedron is the icosahedron, the 600-cell is sometimes called the “hypericosahedron,” That might lead one to think that the cells of a 600-cell are icosahedra, though, and they are actually tetrahedra. These tetrahedra meet twenty at a vertex. I…
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New video: 'Visualizing the 600-Cell': Mathematician/geometer Dugan Hammock of Quantum Gravity Research shows us a visualization of the 4-dimensional 600-Cell projected to 3D object (further projected, technically, to 2D on his computer screen.)
The 600-Cell is a 4-dimensional shape made of 600 tetrahedra. When the Gosset polytope is projected from E8 to 4D at a certain angle, two 600-Cells are produced, the ratio of their sizes being the golden ratio.
VIDEO LINK: https://youtu.be/LMG-jvLoepE
600 Undulating Tetrahedra This is a 600-cell, one of the regular polychora (four-dimensional polytopes), with its edges and vertices rendered invisible, and its cells shrunk so that they do not touch.