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

In this section, we will prove that our pentagon is equiangular by setting up a golden ratio argument: square of (purple line  +  red line)  +  square of red line  =  3 x the square of the purple line. This ratio will be repeatedly applied to lines with greater lengths.

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