Merkabah Openscad

thingiverse

Four specific Cartesian coordinates determine the exact placement of each vertex within this intricate tetrahedron. Its edge length measures a precise 2 units, with its center positioned perfectly at the origin. To establish these points, one starts by calculating the unique combination of x and y values, where x represents the horizontal axis, y signifies the vertical axis, while z denotes the depth dimension. A crucial formula comes into play here: x^2 + z^2 = 1 and y^2 + z^2 = 1. These equations allow for the calculation of each coordinate with pinpoint accuracy. In more detail, two unique coordinates describe each of these tetrahedron vertices: At the horizontal plane's midpoint on either side (±1,0,-1/√2), where 'y' equals 0. Next at mid-z (or depth) planes perpendicular to 'z,' they intersect respectively with y as ±1. The point (x=0,y=±1,z=1/√2).