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

First, we construct a line (in red) from the midpoint of the square to the midpoint of one side of the pentagon, which is parallel to the Cube-to-Pentagon Connection Lines on the left square.

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