Conventionally, Orders of Magnitude are multiples of 10.
Shapes of Magnitude however, define volumes in 3D space and are thus of geo-metric relevance. Conceptually, they are “Metric Containers” in Space, e.g.
3D Cubes – the fundamental Difference of Definition:-
- 1 x 1 x 1 as Digital and Orthogonal Unit – in contrast to
- a x b x c as the generalised algebraic formula.
3D Spheres – as 3D Containers for 2D Shapes:-
- Double Cones and Octagons are “Digitally Metric” 2D Shapes in contrast to
- 4 / 3 x 13 x π as Spherical Unit –
in addition to conventional 3D Polygons or Platonic Solids:
- Tetrahedron – 4 faces;
- Cube – 6 faces;
- Octahedron – 8 faces;
- Dodecahedron – 12 faces;
- Icosahedron – 20 faces.