Forms of the Plane · 3D
Pyramid of the Tetractys
1 + 3 + 6 + 10 = 20 spheres
Stack the Tetractys: ten spheres, then six in the hollows, then three, then one. Twenty spheres make a tetrahedron, and its base is the Tetractys itself.
- Spheres
- 20
- Layers
- 10 · 6 · 3 · 1
- Shape
- tetrahedron
Turn it in your hands, strike it to hear the chord of its edges, slice it with a plane.
Facts
- 1, 4, 10, 20, 35 … are the tetrahedral numbers: sums of the triangular numbers 1, 3, 6, 10, 15.
- The base layer is exactly the Tetractys: cut the pyramid through its bottom row of spheres and the flat figure returns.
- Every sphere sits in a hollow of the layer beneath: the densest way to stack.
- Cannonballs were stacked like this on warships and in forts.
History and meaning
For the Pythagoreans, 1, 2, 3 and 4 were point, line, surface and solid. The pyramid completes the thought: four layers, and the triangle of ten becomes a body.
Across the dimensions
- Its slice TetractysStack six, three and one in the hollows above the ten: the Tetractys is the base of a pyramid of spheres.
