Are there any good textbooks that consider the properties of solid angles for polytopes? Being not the most well-versed in geometry, I am unsure of where to start looking. Thank you very much!
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2$\begingroup$ I'm not sure about textbooks, but one thing you might want to know is that solid angles for polytopes give a valuation in the same way that volume or "discrete volume" (i.e., lattice point counts) do, so that much of the general theory of valuations on convex polytopes can be used to understand solid angles. See e.g. papers by Macdonald and McMullen from the 70s. $\endgroup$– Sam HopkinsCommented Jul 28, 2021 at 20:15
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1$\begingroup$ This may be of help: Desario, David, and Sinai Robins. "Generalized solid-angle theory for real polytopes." Quarterly Journal of Mathematics 62, no. 4 (2011): 1003-1015. arXiv version. They extend work of Macdonald, mentioned by @SamHopkins. $\endgroup$– Joseph O'RourkeCommented Jul 28, 2021 at 20:29
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2$\begingroup$ M. Berger, Geometry. $\endgroup$– Alexandre EremenkoCommented Jul 29, 2021 at 0:16
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$\begingroup$ Can you give an example of such a property, or an analog for 3-d solid angles? $\endgroup$– user44143Commented Jul 29, 2021 at 17:54
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1$\begingroup$ Thank you all very much for the references! They give a lot to explore. @MattF. For an example of a property, a generalization of the sum of interior angles can be found here, although admittedly it does also reference the same paper referred by Joseph. $\endgroup$– riankoCommented Jul 29, 2021 at 23:28
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