computer-controlled cutting (Feb 6)

Regular Polyhedra. Platonic Solids Within the laser cutting exercise I perform a practice to bring 3D geometry to  schoolchildren in Seville. Geometry, spatial vision, the concept of the three-dimensional display is not welcomed  because of new technologies (film, television, video games). Educational programs have  not assimilated this concept until an advanced age and curricula already directed  towards technical studies. The purpose of this practice, focused on the development of Computer-Controlled  Cutting and regarding my final work is focused on the development of the five regular  polyhedra exist: hexahedron, icosahedron, dodecahedron, octahedron and tetrahedron.  This practice is aimed at children aged 10-14 years, an age where no special requires  geometric knowledge in schools, but the kids interested and want to start learning more. In design practice, a historical approach allows children to know that regular polyhedra  were known in ancient Greece. Com that Plato used symbols of his philosophy, and  each represents earth, air, fire and water, combining the tetrahedron to the fifth element  or spiritual entity.  I get to practice with children who talk philosophy and mathematics, but without being  heavy for them.  The amount of software to represent geometric figures is wide. In Andalusia schools  students have computers running Ubuntu which include this software. But for the  development of this practice is better than software suits Fab Academy.  In the example shown in the image, use the golden rectangle to generate an  icosahedron from Rhinoceros. It is a quick exercise to show students. The development of laser cutting exercise I have chosen the program Inkscape, which  helps with your clone tool to play with the tabs and get a correct fit of the faces of the  polyhedra.  In developing the model, the part that I'm most happy is the union of the edges,  developed to serve in the construction of all regular polyhedra, preventing exists a model  for every angle, all being in the same room , saving material and space for a more  elaborate design generate a wrapper that allows to keep all the pieces together to store  or move.  The circular piece is marked in each angle corresponding to each polyhedron and  facilitates assembly of the final model using the following numerical relationship: Piece nº 1. Tetrahedron.  4 faces (equilateral triangles). 4 vertices. Common point of three faces.  6 edges. Concurren three at each vertex.  Dihedral angle of 70 32 '.  Piece nº 2. Cube.  6 guys (cuadrados). 8 vertices. Common point of three faces.  12 edges. Concurren three at each vertex.  Dihedral angle of 90. Piece nº 3. Octahedron.  8 faces (equilateral triangles). 6 vertices. Common point of four faces.  12 edges. Concurren four at each vertex.  Dihedral angle of 109 28 '.  Piece nº 4. Dodecahedron.  12 faces (regular pentagons). 20 vertices. Common point of three faces.  30 edges. Concurren three at each vertex.  Dihedral angle of 116 34 '. Piece nº 5. Icosahedron.  20 faces (equilateral triangles). 12 vertices. Common point of five guys.  30 edges. Concurren five in each vertex.  Dihedral angle of 138 11 '. Modelo preparado para corte:  During design development, the main problem I had was choosing the sizes of the tabs  and their number per edge. I chose 3 mm MDF material to cut and started designing  parts with two tabs per edge. These two faces are oversized for the final result, so  eyelashes went from two to one per edge.  The result is a pattern of regular polyhedra physical representation that allows the child  to play with their mounting, known characteristics of each (sides, edges, angles, corners,  etc.) and be the beginning of the spatial geometry designed by computer.   Algunos ejemplos de las piezas terminadas: To improve the design: - Container box and engraved on the faces of the polyhedra characteristics and number.  - Increased size of the faces.  Software used: - Photoshop. - Inkscape - Gimp - Rhinoceros - sketchup