Monthly Archives: October 2020

Closed-form numbers

Recall that the logarithm function (defined on the punctured complex plane) is multi-valued, with the different solutions to exp(x) = y differing by integer multiples of 2πi.   James Propp remarked that the values of the form i^i^i are a … Continue reading

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The Barnes-Wall lattices

For any nonnegative integer n, there exists the highly symmetric Barnes-Wall lattice in dimension . In low dimensions, these are (up to scaling and rotation) familiar lattices: For n = 0, this is just the integer lattice, . For n … Continue reading

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Subsumptions of regular polytopes

We say that a regular n-dimensional polytope P subsumes a regular n-dimensional polytope Q if the vertex-set of Q is geometrically similar to a subset of the vertex-set of P. For instance, the dodecahedron subsumes a cube (the convex hull … Continue reading

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