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
As previously stated, using the Golden Ratio Property:

square of yellow line  +    square of smaller segment
   =    3 x square of larger segment.

But:
square of yellow line   +   square of purple line
= square of cyan line.

Thus:
square of cyan line = 3 x square of green line.

Hence:
square of cyan line   +   square of green line
= 4 x square of green line.
Back To Main Page