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Nov 29, 2023 at 0:51 comment added Iosif Pinelis @NateRiver : You are very welcome. Even for triangles on the plane, it is a quadruple integral, whose completely specified version took Mathematica about half an hour to compute. So, it was actually a bit surprising to me that this quadruple integral in general can be reduced to an ordinary integral.
Nov 28, 2023 at 23:10 vote accept Nate River
Nov 28, 2023 at 23:03 comment added Nate River Thank you very much for the complete answer. I am very surprised that even the triangles in $\mathbb R^2$ case is this complicated.
Nov 28, 2023 at 20:54 history edited Iosif Pinelis CC BY-SA 4.0
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Nov 28, 2023 at 14:52 history answered Iosif Pinelis CC BY-SA 4.0