In
geometry, an omnitruncation of a
convex polytope is a
simple polytope of the same dimension, having a vertex for each
flag of the original polytope and a
facet for each face of any dimension of the original polytope. Omnitruncation is the
dual operation to
barycentric subdivision.[1] Because the barycentric subdivision of any polytope can be realized as another polytope,[2] the same is true for the omnitruncation of any polytope.
^Matteo, Nicholas (2015), Convex Polytopes and Tilings with Few Flag Orbits (Doctoral dissertation), Northeastern University,
ProQuest1680014879 See p. 22, where the omnitruncation is described as a "flag graph".
^Ewald, G.; Shephard, G. C. (1974), "Stellar subdivisions of boundary complexes of convex polytopes", Mathematische Annalen, 210: 7–16,
doi:
10.1007/BF01344542,
MR0350623