The Geometry Behind the Forms
Established mathematics first. Where a shape carries spiritual or historical meaning, it is labelled as interpretation — not presented as scientific fact.
How extrusion creates volume
An outline is swept along the Z axis. Each ring becomes an annulus — an outer and an inner circle — joined by side walls, with optional bevels on the edges.
Circles and intersections
Two circles of radius r with centres d apart meet at two points when d < 2r. The intersection lies at a = d/2 from either centre, at height h = √(r² − a²). Every intersection in this site is solved this way, not drawn by hand.
Open in the viewer →Symmetry and rotational order
The Seed of Life looks the same after any rotation of 60°: its rotational order is 6. With its six mirror lines it belongs to the dihedral group D6 — the symmetry of a regular hexagon.
Open in the viewer →Regular polygons
Joining neighbouring centres of the hexagonal circle grid reveals equilateral triangles and regular hexagons, the only regular polygons besides squares that tile the plane.
Open in the viewer →Platonic solids & tetrahedral geometry
There are exactly five convex regular polyhedra. The tetrahedron — four triangles — is the simplest. Two of them, interpenetrating, form the stella octangula, whose shared core is an octahedron.
Open in the viewer →Polyhedral structures
The cuboctahedron is Archimedean: two kinds of regular face meet identically at every vertex. Its 12 vertices sit exactly one edge-length from the centre, as spheres do in close packing.
Open in the viewer →Projection from 3D to 2D
Flattening a solid along an axis keeps x and y but discards depth. Viewed down its three-fold axis, the cuboctahedron becomes a hexagonal pattern familiar from sacred geometry art.
Open in the viewer →