Today I Learned

Some of the things I've learned every day since Oct 10, 2016

11: Self-Dual Polytopes

The dual structure of an n-dimensional  polytope is the result of exchanging each (k-1)-face for an (n - k)-face for k = 1 \dots n-1, while maintaining the original connectivity between these. If this resulting structure is similar to the original polytope, the polytope is said to be self-dual.

Examples of self-dual polytopes include all regular 2-polytopes (regular polygons), and all regular simplices (equilateral triangles, regular tetrahedrons, etc.).

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