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
The Golden Ratio argument can be transformed into:
square of purple line  +  square of red line  = 
3 x square of blue line

Thus,
square of purple line  +  square of red line  +  square of blue line
= 4 x square of blue line

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