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A self-dual polytope is a polytope whose dual is isomorphic to itself. The number of elements of a dual polytope follow a palindromic pattern. The facets of a self-dual polytope are equivalent to the dual of its vertex figure(s). A self-dual polytope that is also isogonal is also isotopic, making it a noble polytope.
The self-dual regular polytopes are the regular polygons in two dimensions, the simplexes in any dimension, and the icositetrachoron, great hecatonicosachoron, and grand stellated hecatonicosachoron in four dimensions. The regular hypercubic honeycomb of any dimension is also self-dual.
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