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A zonohedron is a convex polyhedron with point symmetry, every face of which is a polygon with point symmetry.Any zonohedron may equivalently be described as the Minkowski sum of a set of line segments in three-dimensional space, or as the three-dimensional projection of a hypercube.Zonohedra were originally defined and studied by E. S. Fedorov, a Russian crystallographer.

en.wikipedia.org/wiki/ZonohedronA hypercube can be defined by increasing the numbers of dimensions of a shape: 0 – A point is a hypercube of dimension zero. 1 – If one moves this point one unit length, it will sweep out a line segment, which is a unit hypercube of dimension one. 2 – If one moves this line segment its length in a perpendicular direction from itself; it sweeps out a 2-dimensional square.

simple.wikipedia.org/wiki/HypercubeZonotopes: From Guaranteed State-estimation to Control - Kindle edition by Vu Tuan Hieu Le, Cristina Stoica, Teodoro Alamo, Eduardo F. Camacho, Didier Dumur. Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Zonotopes: From Guaranteed State-estimation to Control.

Zonotopes: From Guaranteed State-estimation to Con...The Nash–Moser theorem, attributed to mathematicians John Forbes Nash and Jürgen Moser, is a generalization of the inverse function theorem on Banach spaces to a class of "tame" Fréchet spaces

en.wikipedia.org/wiki/Nash–Moser_theoremThe maximum volume for a given surface (or, equivalently, the minimum surface for a given volume) is obtained when the differential forms dV amd dS are proportional (the coefficient of proportionality is the Lagrange multiplier associated to whichever quantity is considered a constraint under which the other is to be optimized). Thus, the distance between A and B must vanish.

www.numericana.com/answer/polyhedra.htm