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

And since the purple lines are equal to each other, and the red lines are equal to each other, the golden ratio property can be transformed once again on the next page.

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