Construction of a Pentagon on the cube Proof of Part I: Pentagon is Equilateral Proof of Part II: Pentagon is in One Plane Proof of Part III: Pentagon is Equiangular Proof of Part IV: Side of Dodec Form Apotome Construction of the Dodecahedron

Since the sum of green and purple line equals the yellow line, and the green line equals the green perpendicular Cube-to-Pentagon Connector line. Moreover, using the Golden Ratio Property: the square of the whole line  +   the square of the smaller segment    =    3 x the square of the larger segment.

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