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Let

and

be the centers of the two adjacent cube faces

and

with common side

, and let

, and

be the midpoints of

, and

are points that satisfy the golden section conditions

, and

and

are perpendicular to

is perpendicular to

, and

is one face of a regular dodecahedron.

The other faces are constructed in the same way.

Contributed by: Milana Dabic

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Euclid's Construction of a Regular Dodecahedron (XIII.17)