Generalized Heron's formula for n-dimensional "n-angle" instead of "triangle"

Question

Is there a generalized version of Heron's formula for calculating the equivalent of a "volume" of an n-dimensional "n-angle" based on the length of it's sides? I've seen the equivalent formula for a tetrahedron, but I'd like to keep extending the shape by adding an extra point that connects to all existing points in the next dimension.

Does that make sense?

n-angle $\mapsto$ simplex $:$ ? $;;;$ – Oct 09 '13 at 05:11 — , Oct 09 '13 at 05:11

score 11 · Accepted Answer · answered Oct 09 '13 at 05:19

11

Yes. See Cayley-Menger Determinant

answered Oct 09 '13 at 05:19

Robert Israel

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Generalized Heron's formula for n-dimensional "n-angle" instead of "triangle"

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