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

Furthermore, by construction, all four of these perpendicular lines is equal to the red line segment on the square on the right hand side, which is the greater segment of the extreme and mean ratio.

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