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  "body": "\n## Summary\n\nThe Wythoff construction builds a polytope from a finite reflection group and a chosen point.\nOne takes a point in the fundamental region of the group and reflects it in the mirrors over and over.\nThe convex hull of all the images is the polytope.\nChoosing which mirrors the point lies on gives the regular polytopes, their truncations and most other [[uniform polytopes|BZXHGNGQAX]] with the same symmetry.\nIt ties the geometry of polytopes to the combinatorics of [[Coxeter groups|G6FND7X69J]].\n\n## Explanations\n\n### L1 human\n\nThink of a kaleidoscope: a few mirrors meeting at angles like $90^\\circ$ or $60^\\circ$.\nPut a single dot between the mirrors and look at all its reflections; then join up the dots into a solid.\nIf the dot sits on some of the mirrors, its images merge, and one gets for instance a cube or an octahedron.\nIf it sits at a well-chosen place between the mirrors, one gets a truncated shape such as the regular octagon from the mirrors of a square.\n",
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