I wrote: << . . . but should have worded the last sentence as: << Again the p-otenuse has one right corner at the origin of the positive orthant, and the rest of them must be "p-acute" -- defined by requiring that each angle between two edges emanating from this corner is acute.

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But more to the, uh, point: each dihederal angle between two hyperplanes bounding the p-otenuse is acute. --Dan