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
Construction of a Dodecahedron

Our project consists of 5 main sections.

We will start off by showing the construction of a vital element of a dodecahedron, which consists of a pentagon lying on two sides of the cube.

Then, we will proof that by following the above construction method, the following properties result:
  1. Proof I: The Constructed Pentagon is Equilateral.
  2. Proof II: The Constructed Pentagon is in One Plane.
  3. Proof III: The Constructed Pentagon is Equiangular.
  4. Proof IV: The Side of the Dodecahedron is the Irrational Straight Line called Apotome.
Finally, by duplicating this element of the dodecahedron, we show the construction of the dodecahedron.


Please use the navigation bar above to look at the proofs in each section.


For Reference, Here are the links to the postscript file:
  1. Construction of a Pentagon on the 2 sides of the cube
  2. Proof of Part I: Pentagon is Equilateral
  3. Proof of Part II: Pentagon is in One Plane
  4. Proof of Part III: Pentagon is Equiangular
  5. Proof of Part IV: Side of Dodecahedron Form Apotome
  6. Construction of the Dodecahedron
Back To Main Page