Most of the construction was done with hand tools. Joints were form-fitted using specially designed adzes like the one above.
Squares are facets of the cube -- 1
Triangles are facets of the octahedron/tetrahedron -- square root of 2
Diamonds are facets of the rhombic dodecahedron -- square root of 3,
the true diamond shape, with angle, 109° 27’ 16”, the diamond bond angle.