The angles between adjacent spokes in the diamond crystal, where four spokes always meet in a uniform configuration, are always exactly 109 degree 28 minutes (109° 28’). Looking at the corner of the cube unit cell, along the axis of a spoke, reveals angles of exactly 120°, which is the included or face angle of the regular hexagon. As is well know this hexagonal geometry is a pervasive pattern in natural structure. Also, in the world of everyday experience, the regular hexagon is commonly used for floor tiling and pavers.
View of diamond crystal looking at the cube corner reveals an inherent hexagonal assembly, exhibiting 120° angles. Extending the ball spoke model to eight unit cells further emphasizes the hexagonal geometry of the structure.
Looking at the edge of the cubic unit cell reveals another aspect of the diamond crystal geometry. A hexagonal structure is apparent in this view, however the angles are not 120 degrees. This view reveals two opposed angles of 109 degrees 28 minutes, and four angles of 115 degrees 53 minutes.
Extended to eight unit cells repeats the hexagonal pattern.
Looking at the square face of the cubic unit cell reveals another aspect of the diamond crystal geometry. A repeating pattern of perfect squares is presented in which the squares are rotated 45 degrees so that their edges are parallel to the diagonal of the basic cube unit cell.
Extended to eight unit cells repeats the square pattern.
If we look at the ball and spoke model along an axis parallel to a set of spokes, as we did earlier, regular hexagons are revealed, along with equilateral triangles. If we map the diamond geometry with the ball and spoke model within the Curved Space tunnel labyrinth along that same view axis, we see a corresponding geometry.
Here we see the tunnel labyrinth without the ball and spoke mapping.
Extending the tunnel labyrinth to 8 unit cells creates a seemingly complex three dimensional structure comprised of continuous surfaces.
With the ball and spoke mapping.