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Mean Tetrahedron Volume

The mean tetrahedron volume V^_ is the average volume of a tetrahedron in tetrahedron picking within some given shape. As summarized in the following table, it is possible to compute the mean tetrahedron volume in closed form for tetrahedron picking for some simple shapes.

shapeV^_
ball tetrahedron picking(12pi)/(715)
cube tetrahedron picking(3799)/(216000)-(pi^2)/(2160)
octahedron tetrahedron picking approx 0.01368
sphere tetrahedron picking(4pi)/(105)
tetrahedron tetrahedron picking(13)/(720)-(pi^2)/(15015)

See also

Mean Line Segment Length, Mean Triangle Area, Tetrahedron Picking

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Cite this as:

Weisstein, Eric W. "Mean Tetrahedron Volume." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MeanTetrahedronVolume.html

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