If you are mathematically inclined and want to learn more about the geometry of close-packing of spheres - read the current version of the white paper available below. The list below is based on this document:

We value your opinions and suggestions - Please provide feedback.

Platonic Structures - How to Series

• Part 1: Introduction

  • 01. Platonic Structures (3:13 min)
  • 02. The Platonic Box (1:30 min)
  • 03. Assembling a Platonic Structure (0:35 min)
  • 04. Platonic Structures - Getting to Know Me (4:24 min)
  • 05. How to assemble a Rhombic Dodecahedron node (2:16 min)
  • 06. The Injection Mold (1:41 min)

Platonic Structures Series - Educational Videos

• Part 1: Close Packing of Spheres

  • 01. A Sphere and its Twelve Neighbors (2:25 min)
  • 02. The Square Lattice (2:24 min)
  • 03. The Hexagonal Lattice (2:49 min)
  • 04. Square Pattern - Planes Periodicity (1:35 min)
  • 05. Hexagonal Pattern - Planes Periodicity (2:26 min)
  • 06. Orthogonal Planes and Axes (2:33 min)
  • 07. Tetragonal Planes and Axes (2:48 min)

• Part 2: Platonic Solids

  • 08. Platonic Solids - Introduction (3:12 min)
  • 09. PlatonicSolids - Tetrahedron (2:08 min)
  • 10. Platonic Solids - Octahedron (2:35 min)
  • 11. Platonic Solids - Cube (2:19 min)
  • 12. Platonic Solids - Icosahedron (4:34 min)
  • 13. Platonic Solids - Dodecahedron (4:43 min)

• Part 3: Minimum Surfaces

  • 14. Minimum Surfaces - Rhombic Dodecahedron (3:02 min)
  • 15. Minimum Surfaces - Soap Film Like Surfaces in CPS (5:42 min)
  • 16. Minimum Surfaces - Other Releated Solids (2:36 min)
  • 17. Minimum Surfaces - Intersection Lines (2:29 min)

• Part 4: Archimedean Solids

  • 18. Archimedean Solids - The Cuboctahedron from Identical Spheres (2:37 min)
  • 19. Archimedean Solids - Truncated Tetrahedron from Identical Spheres (3:05 min)
  • 20. Archimedean Solids - Truncated Octahedron from Identical Spheres (2:31 min)
  • 21. Archimedean Solids - Truncated Cube from Identical Spheres (6:18 min)
  • 22. Archimedean Solids - Truncated Icosahedron from Identical Spheres (4:46 min)

• Part 5: Ratios and Similarity

  • 23. CPS Geometry - The Mental-Experimental Method (4:20 min)
  • 24. CPS Geometry - From Spheres to Geometrical Points (5:18 min)
  • 25. CPS Geometry - Similarity Theorem in CPS (11:06 min)
  • 26. CPS Geometry - The Golden Section and the Fibonacci Sequence - 1 (11:09 min)
  • 27. CPS Geometry - The Golden Section and the Fibonacci Sequence - 2 (9:17 min)

• Part 6: Lines in CPS

  • 28. CPS Geometry - Lines Patterns in Space (8:51 min)
  • 29. CPS Geometry - The Incommensurables (9:43 min)
  • 30. CPS Geometry - The Square Root Spiral (10:41 min)
  • 31. CPS Geometry - Square Root Lines (9:03 min)
  • 32. CPS Geometry - The Proof for Riemann Hypothesis? - Part 1 (13:56 min)




• Appendices

  • Appendix A - Experimenting with Close Packing Of Spheres (1:35 min)