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  "body": "\n## Summary\n\nA regular polytope is a polytope with the largest possible symmetry: its symmetries can carry any flag of faces to any other flag.\nIn the plane the regular polytopes are the [[regular polygons|01KJJ9A400]], and in space the convex ones are the five [[Platonic solids|017E5PRS1Q]].\nEach regular polytope is described by its [[Schläfli symbol|MAE6BF4DFK]], and their full list is given by the [[classification of regular polytopes|XYCD53PB5K]].\nRegular polytopes are the model objects of the theory of polytopes and of finite reflection groups.\n\n## Explanations\n\n### L1 human\n\nA regular polytope looks the same from every corner, every edge, every face, and so on.\nMore precisely, pick a corner, an edge at that corner, and a face at that edge; any such choice can be moved to any other by a symmetry.\nThe cube is regular: any corner, edge and face that fit together can be rotated or reflected to any other such triple.\nA box with sides of three different lengths is not regular, because a short edge cannot be moved onto a long one.\n",
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