5. Angle & Pattern Study

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.

5a_01c -- 00 Hex View SINGLE Spoke End_CUBE 5b_01a -- 00 Hex View SINGLE Spoke End

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.

5c_08c -- 00 Hex View NETWORK Spoke End_CUBE 5d_08a -- 00 Hex View NETWORK Spoke End

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.

5e_01c Edge View Single Cell CUBE 5f_01a Edge View Single Cell copy

Extended to eight unit cells repeats the hexagonal pattern.

5g_08c Edge View Full Network CUBE 5h_08a Edge View Full Network copy

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.

5i_01c Vace View Single Cell CUBE 5j_01a Vace View Single Cell

Extended to eight unit cells repeats the square pattern.

5k_08c Vace View Full Network CUBE 5l_08a Vace View Full Network

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.

5m_Hexagon End View With Ball and Spoke Only 5n_Hexagon End View With Trapsparent Fillte Spoke

Here we see the tunnel labyrinth without the ball and spoke mapping.

5o_Hexagon End View With Exanded and Filleted Spoke Only OPAQUE

Extending the tunnel labyrinth to 8 unit cells creates a seemingly complex three dimensional structure comprised of continuous surfaces.

5p_Hexagon End View With Exanded and Filleted Spoke Only OPAQUE NETWORK

With the ball and spoke mapping.

5q_Hexagon End View With Trapsparent Fillte Spoke NETWORK

Advertisements