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I’m not sure what you mean. The shapes in the article do not have corners by the definition I would use… they do have edges and it left me wondering if you coul

• MiddleEndian 2y ago
  >it left me wondering if you could tile 3d space with edge-free shapes. Probably not, but maybe a 4D space lol
• mdp2021 2y ago
  > corners by the definition I would use You would speak of "vertexes". Tile a 3d space with cubes: you'll have faces, edges and vertexes. Curve the edges in smooth paths ("with continuous derivatives"): the vertexes disappear. But the equivalent of the 2d "corners" remain, as apparent in the 2d sections: no miracle happens. The interesting part is the induction that by adding a dimension we may lose a "constraint".