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CPS

Part 2 – Platonic Solids

8. Introduction - Platonic Solids And CPS 9. The in CPS 10. The in CPS 11. The in CPS 12. The Icosahedron in CPS 13. The Dodecahedron in CPS

Nick Trif

Ottawa, Ontario, Canada – 2018 www.platonicstructures.com CPS Geometry Part 2 – Platonic Solids – 10: The Octahedron from Spheres

YouTube: https://youtu.be/s6hFZzlIADc The octahedron pattern is again relatively easy to spot in the Close Packing of Sphere arrangement. The octahedron pattern is again relatively easy to spot in the Close Packing of Sphere arrangement. Starting from a pattern, a square can be constructed in a very direct way - just stuck smaller and smaller square planes on top of each other, until you get to the top. 2 Layers Starting from a square pattern, a square pyramid can be constructed in a very direct way - just stuck smaller and smaller square planes on top of each other, until you get to the top. 3 Layers Starting from a square pattern, a square pyramid can be constructed in a very direct way - just stuck smaller and smaller square planes on top of each other, until you get to the top. 5 Layers Starting from a square pattern, a square pyramid can be constructed in a very direct way - just stuck smaller and smaller square planes on top of each other, until you get to the top. 6 Layers Starting from a square pattern, a square pyramid can be constructed in a very direct way - just stuck smaller and smaller square planes on top of each other, until you get to the top. 8 Layers Starting from a square pattern, a square pyramid can be constructed in a very direct way - just stuck smaller and smaller square planes on top of each other, until you get to the top. 9 Layers Starting from a square pattern, a square pyramid can be constructed in a very direct way - just stuck smaller and smaller square planes on top of each other, until you get to the top. 10 Layers Starting from a square pattern, a square pyramid can be constructed in a very direct way - just stuck smaller and smaller square planes on top of each other, until you get to the top. 11 Layers Starting from a square pattern, a square pyramid can be constructed in a very direct way - just stuck smaller and smaller square planes on top of each other, until you get to the top. 12 Layers Starting from a square pattern, a square pyramid can be constructed in a very direct way - just stuck smaller and smaller square planes on top of each other, until you get to the top. 13 Layers Two such square pyramids, having the same base and developing in two opposite directions, generate the second , the octahedron. Two such square pyramids, having the same base and developing in two opposite directions, generate the second platonic solid, the octahedron. Two such square pyramids, having the same base and developing in two opposite directions, generate the second platonic solid, the octahedron. These days, we have at our disposal powerful tools to produce 3-D Visualizations and Animation of 3-D structures that theoretically are identical with the real objects. These days, we have at our disposal powerful tools to produce 3-D Visualizations and Animation of 3-D structures that theoretically are identical with the real objects. These days, we have at our disposal powerful tools to produce 3-D Visualizations and Animation of 3-D structures that theoretically are identical with the real objects. These days, we have at our disposal powerful tools to produce 3-D Visualizations and Animation of 3-D structures that theoretically are identical with the real objects. These days, we have at our disposal powerful tools to produce 3-D Visualizations and Animation of 3-D structures that theoretically are identical with the real objects. There is still some limitation with this approach; one cannot escape the fact that these 3-D models are "virtual". These days, we have at our disposal powerful tools to produce 3-D Visualizations and Animation of 3-D structures that theoretically are identical with the real objects. There is still some limitation with this approach; one cannot escape the fact that these 3-D models are "virtual". These days, we have at our disposal powerful tools to produce 3-D Visualizations and Animation of 3-D structures that theoretically are identical with the real objects. There is still some limitation with this approach; one cannot escape the fact that these 3-D models are "virtual". When very complex structures, assembled from thousand of spheres, are seen on a 2-D screen, they become difficult to manipulate and tricky to see and grasp some of their details. When very complex structures, assembled from thousand of spheres, are seen on a 2-D screen, they become difficult to manipulate and tricky to see and grasp some of their details. With all these limitations, this is the preferred method used to present the C.P.S. structures and patterns in this video and on our web-site: www.platonicstructures.com These days, we have at our disposal powerful tools to produce 3-D Visualizations and Animation of 3-D structures that theoretically are identical with the real objects. Again, with a little bit of imagination, we can assemble variation of the square pyramids, and implicitly the octahedron. Again, with a little bit of imagination, we can assemble variation of the square pyramids, and implicitly the octahedron. Again, with a little bit of imagination, we can assemble variation of the square pyramids, and implicitly the octahedron. The best way to completely investigate structures and patterns that can be formed using close-packing of spheres is to assemble and to build real 3-D structures. The best way to completely investigate structures and patterns that can be formed using close-packing of spheres is to assemble and to build real 3-D structures. The best way to completely investigate structures and patterns that can be formed using close-packing of spheres is to assemble and to build real 3-D structures. Nothing compares with having a real structure in your hands. Nothing compares with having a real structure in your hands. The best way to see the complex platonic structures in your mind is to play with the real platonic structures using your hands. This is where the real 3-D Platonic Structures come into play. The best way to see the complex platonic structures in your mind is to play with the real platonic structures using your hands. www.platonicstructures.com

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