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 – 19: Truncated Tetrahedron from Spheres
YouTube: https://youtu.be/ss2dJN0Q2u8 Starting from a tetrahedron, one can generate a truncated tetrahedron in two steps: Starting from a tetrahedron, one can generate a truncated tetrahedron in two steps: 1. Divide each edge of the tetrahedron in three equal parts; Starting from a tetrahedron, one can generate a truncated tetrahedron in two steps: 1. Divide each edge of the tetrahedron 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 four vertices of the Tetrahedron transform in 4 triangular faces, and the triangular faces of the initial solid become hexagonal faces. When starting from a tetrahedron assembled from identical spheres, one can generate a truncated tetrahedron by removing spheres forming the vertices of the platonic solid. One can observe that, the truncated tetrahedron has two types of edges. One can observe that, the truncated tetrahedron 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 triangular face and a hexagonal face. It can be seen clearly that the new solid has: 8 Faces; 12 Vertices; and 18 Edges. All eight faces have an underlining hexagonal lattice. As seen before for some other patterns in CPS, one can build the truncated tetrahedron as a platonic structure. Using this view, the process of going from the tetrahedron to truncated tetrahedron can be seen in a new light. Using this view, the process of going from the tetrahedron to truncated tetrahedron can be seen in a new light. One can see that a relatively complex geometrical problem has been transformed into a game, or better said, into a toy. One can see that a relatively complex geometrical problem has been transformed into a game, or better said, into a toy. This process can be applied to tetrahedrons formed from a fewer numbers of spheres. The truncated tetrahedron pattern can still be seen clearly in this simple structure. This process works on any tetrahedron with the edges divisible in three equal sizes. This requires the edge of the tetrahedron to have a well defined number of spheres.
This number shall be one of the following: 4, 7, 10, 13 and so on. Let's start by stating a well known fact: A sphere can be completely surrounded by exactly twelve others identical spheres, in only one way. Looks like complex patterns can only be formed from specific number of spheres. This could hint to a possible way to explain the quantization of space and the quantum phenomena, in general.
I hope to say more about this in a future presentation. www.platonicstructures.com
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