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, we construct
a line (in red)
from the midpoint of the square to the midpoint of one side of the pentagon, which is parallel to the Cube-to-Pentagon Connection Lines on the left square.
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