CPS Geometry Part 4 – Archimedean Solids 18. The Cuboctahedron in CPS 19. Truncated Tetrahedron in CPS 20. Truncated Octahedron in CPS 21. Truncated Cube in CPS 22. Truncated Icosahedron in CPS Nick Trif Ottawa, Ontario, Canada – 2018 www.platonicstructures.com CPS Geometry Part 4 – Archimedean Solids – 20: Truncated Octahedron from Spheres YouTube: https://youtu.be/fjEd_Ty5lKA The process of generating a truncated tetrahedron from a tetrahedron, can also be used to generate a truncated octahedron. The process of generating a truncated tetrahedron from a tetrahedron, can also be used to generate a truncated octahedron. Of course, we have to start from an octahedron this time. The same two steps have to be followed: 1. Divide each edge of the octahedron in three equal parts; The same two steps have to be followed: 1. Divide each edge of the octahedron in three equal parts; 2. Cut the vertexes of the platonic solid with planes determined by the divisions done in the first step. The same two steps have to be followed: 1. Divide each edge of the octahedron in three equal parts; 2. Cut the vertexes of the platonic solid with planes determined by the divisions done in the first step. The same two steps have to be followed: 1. Divide each edge of the octahedron in three equal parts; 2. Cut the vertexes of the platonic solid with planes determined by the divisions done in the first step. By doing these, the six vertices of the Octahedron transform in 6 square faces. By doing these, the six vertices of the Octahedron transform in 6 square faces. The eight triangular faces of the initial solid become eight hexagonal faces. In CPS, when starting from an Octahedron assembled from identical spheres, one can generate a truncated octahedron by removing spheres forming the vertices of the platonic solid. In CPS, when starting from an Octahedron assembled from identical spheres, one can generate a truncated octahedron by removing spheres forming the vertices of the platonic solid. The truncated Octahedron has two types of edges. The first type of edges is formed between two hexagonal faces. The truncated Octahedron has two types of edges. The first type of edges is formed between two hexagonal faces. The second type of edges is formed between a square face and a hexagonal face. It can be seen clearly that the new solid has: 14 Faces; 24 Vertices; and 36 Edges. This process can be applied to Octahedrons formed from a fewer numbers of spheres. This process can be applied to Octahedrons formed from a fewer numbers of spheres. This process can be applied to Octahedrons formed from a fewer numbers of spheres. The Truncated Octahedron pattern can still be seen clearly in this simple structure. The Truncated Octahedron pattern can still be seen clearly in this simple structure. The Truncated Octahedron pattern can still be seen clearly in this simple structure. This process works on any Octahedron with the edges divisible in three equal sizes. This process works on any Octahedron with the edges divisible in three equal sizes. This process works on any Octahedron with the edges divisible in three equal sizes. This process works on any Octahedron with the edges divisible in three equal sizes. The number of spheres determining the initial octahedron must be one of the following: 4, 7, 10, 13 and so on. The number of spheres determining the initial octahedron must be one of the following: 4, 7, 10, 13 and so on. The number of spheres determining the initial octahedron must be one of the following: 4, 7, 10, 13 and so on. Looks like the quantization of space is inherited in our initial assumption: “the points in space are distributed following the close packing of sphere arrangement”. Looks like the quantization of space is inherited in our initial assumption: “the points in space are distributed following the close packing of sphere arrangement”. Looks like the quantization of space is inherited in our initial assumption: “the points in space are distributed following the close packing of sphere arrangement”. www.platonicstructures.com Beauty makes beautiful things beautiful!.