We calculate the distance from the Tetrahedron’s center of volume (COV) to a Tetrahelix symmetry axis passing through the Tetrahedron.

On another web page ( see here ) we calculated the vertex coordinates of a Tetrahedron when part of the Tetrahelix, with the condition that the edge length of the Tetrahedron EL=1, and that one vertex of the Tetrahedron is along the x-axis. We aligned the symmetry axis of the Tetrahelix so that it is the z-axis. The four (x, y, z) coordinates of the Tetrahedron are then given by

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The Tetrahedron’s COV is calculated to be the average of these vertex coordinates. We get

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It doesn’t matter what the z-component is because we want to know the distance from the z-axis to the COV, which is independent of the z-component. But we calculate it anyway.

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The distance from COV = (COV_{X}, COV_{Y},
COV_{Z}) to the z-axis is given by

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When the edge length (EL) is not equal to one, this becomes

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