Platonic Polyhedrons: Poliedros Platnicos

In three-dimensional geometry, a platonic solid is a convex regular polyhedron, made up of several regular and equal polygons in shape and size, therefore all sides are identical, all angles between edges are equal and the length of all its edges are constant. There are only five perfect regular polyhedrons known as the Platonic Solids because the Greek philosopher Plato (427 -347 BC) was who studied them thoroughly and described them for science. They are: the tetrahedron (with 4 vertices, 6 edges and 4 triangular facets), the hexahedron or cube (with 8 vertices, 12 edges and 6 square facets), the octahedron (with 6 vertices, 12 edges and 8 triangular facets), the dodecahedron (with 20 vertices, 30 edges and 12 pentagonal facets) and the icosahedron (with 12 vertices, 30 edges and 20 triangular facets). In this booklet you will find formulas to calculate the main dimensions of each of the Platonic solids or polyhedrons: the height, the surfaces of each facets and total, the total volume and the radius of the circumscribed, inscribed and middle spheres. Also find some pages to trim and build solids that can serve for educative purposes for children and youth or for decoration in your desk or library.-------------------------------- En geometr a tridimensional, un poliedro o un s lido plat nico es un poliedro regular convexo, conformado por varios pol gonos regulares e iguales en forma y tama o, por lo tanto, todas sus caras son id nticas, todos sus ngulos entre aristas son iguales y la longitud de todas sus aristas es constante. Existen solamente cinco poliedros regulares perfectos, conocidos como s lidos plat nicos porque fue el fil sofo griego Plat n (427 - 347 AC) quien los estudi a fondo y los describi para la ciencia. Son ellos: el tetraedro (con 4 v rtices, 6 aristas y 4 caras triangulares), el hexaedro o cubo (con 8 v rtices, 12 aristas y 6 caras cuadradas), el octaedro (con 6 v rtices, 12 aristas y 8 caras triangulares), el dodecaedro (con 20 v rtices, 30 aristas y 12 caras pentagonales) y el icosaedro (con 12 v rtices, 30 aristas y 20 caras triangulares).En este folleto vas a encontrar las f rmulas para calcular las principales dimensiones de cada uno de los s lidos o poliedros plat nicos: la altura, la superficie de cada una de sus caras, la superficie total del s lido, el volumen y los radios de las esferas circunscrita, inscrita y medial. Tambi n encontrar s algunas p ginas para recortar y construir los s lidos que pueden servir con fines educativos para ni os y j venes o para adorno en un escritorio o biblioteca.