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, let's examine the Golden Ratio Division Point on the square on the right hand side. The red line is the greater segment of the extreme and mean ratio, and the purple line is the lesser one. By the Golden Ratio property, we obtain that a proportional relationship: whole line:red line   =    red line:purple line.

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