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

Next, we construct perpendicular lines to the square on the Golden Ratio Division Points. Each of these lines have the length of the greater segment of the extreme and mean ratio, which is the same as the length that runs from the midpoint of the line to the Golden Ratio Division Points. For convenience, we will call these perpendicular lines extended on the Golden Ratio Division Points as "Cube-to-Pentagon Connection Lines".

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