Tetrahedrons & Octahedrons

Sphere to tetrahedron-octahedron couplet
Transition from spheres to

Emergence from spheres and doubling functions:
1. A Study of Numbers: https://81018.com/number/#Kepler
2. Growth: https://81018.com/growth/
3. Emergence: https://81018.com/emergence/
4. Fabric: https://81018.com/fabric/
5. Symmetry: https://81018.com/symmetry/
6. Circles-spheres: https://81018.com/circles-spheres/
7. Stacking: https://81018.com/stacking/
8. Spheres: https://81018.com/sphere/. https://81018.com/spheres/
9. Start: https://81018.com/start/
10. First Instance: https://81018.com/instance/#4b/
11. Tetrahedral Gap: https://81018.com/gap/

Three levels of simple complexity:

1. Observe the tetrahedron in the bottom left corner.

2. Notice that it is enclosed in a larger tetrahedron. Right beside it is
an octahedron, plus there is a tetrahedron in each of the other three corners. Every tetrahedron encloses four “half-sized” tetrahedrons and an octahedron.

3. Notice that our larger tetrahedron is enclosed by an even larger tetrahedron. This pattern repeats itself getting smaller and getting larger. Part of the complexity can be seen by observing the center octahedron. Notice the red, black and blue hexagonal plates. A white plate has been obscured. Each shares the common centerpoint.

4. Notice the octahedron in the middle whereby that center triangle is one of its eight faces. There are four faces that are the center faces of each side of the tetrahedron and there are four interior faces. The octahedron has a half-sized octahedron in each of its eight corners and a tetrahedron in each of these eight faces.

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