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Prove that the x-coordinate of the fifth apex of a regular hexahedron is X5 = (2/3)(x4...

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etotheeyepi | Student, Undergraduate | (Level 1) Valedictorian

Posted November 17, 2012 at 3:08 AM via web

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Prove that the x-coordinate of the fifth apex of a regular hexahedron is

X5 = (2/3)(x4 + x3 + x2) – x1

In this case, the hexahedron is made from two tetrahedrons joined at on face, and the first four x-coordinates are x1, x2, x3, and x4.  X2, x3, x4 are the ponts closest to x5.

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etotheeyepi | Student, Undergraduate | (Level 1) Valedictorian

Posted November 28, 2012 at 2:10 PM (Answer #1)

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A friend of mine gave me this formula.  I have looked at his proof, and I think it only works for a figures with a figure with edges of magnitude equal to 2.

The more general formula would probably have different coeficients.

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