New ask Hacker News story: 24-cells in a 600-cell
24-cells in a 600-cell
2 by johncarlosbaez | 0 comments on Hacker News.
The 24-cell is a four-dimensional regular polytope with 24 vertices and 24 octahedral faces. The 600-cell is a four-dimensional regular polytope with 120 vertices and 600 tetrahedral faces. Since 120/24 = 5, you might hope that there’s a way to partition the 600-cell’s vertices into the vertices of five 24-cells. And there is! A new paper by some high school students shows what we've long believed: there are exactly 10 ways. In fact, they show there are 25 ways to choose some of the vertices of the 600-cell to be the vertices of a 24-cell. These 25 ways can listed in a 5×5 array, so that each row and each column gives one way to partition the 600-cell’s vertices into the vertices of five 24-cells. For details and pictures go here: https://ift.tt/2VhfhQ2
2 by johncarlosbaez | 0 comments on Hacker News.
The 24-cell is a four-dimensional regular polytope with 24 vertices and 24 octahedral faces. The 600-cell is a four-dimensional regular polytope with 120 vertices and 600 tetrahedral faces. Since 120/24 = 5, you might hope that there’s a way to partition the 600-cell’s vertices into the vertices of five 24-cells. And there is! A new paper by some high school students shows what we've long believed: there are exactly 10 ways. In fact, they show there are 25 ways to choose some of the vertices of the 600-cell to be the vertices of a 24-cell. These 25 ways can listed in a 5×5 array, so that each row and each column gives one way to partition the 600-cell’s vertices into the vertices of five 24-cells. For details and pictures go here: https://ift.tt/2VhfhQ2
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