different between permutahedron vs nestohedron

English

permutahedron (plural permutahedrons)

nest +? -o- +? -hedron

nestohedron (plural nestohedra)

(geometry) For a building set B, the Minkowski sum of the simplicies ?_S as S ranges over B. (Here ?_S is the standard simplex of S, i.e., the convex hull of the (nonzero endpoints of the) standard unit vectors e_i for i in S.) Every nestohedron is a generalized permutahedron.

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