A History of Platonic Solids• There are five regular polyhedra that werediscovered by the ancient Greeks.• The Pythagoreans knew of the tetrahedron,the cube, and the dodecahedron; themathematician Theaetetus added theoctahedron and the icosahedron.
These shapes are called the Platonic solids,after the ancient Greek philosopher Plato;Plato, who greatly respected Theaetetuswork, speculated that these five solids werethe shapes of the fundamental componentsof the physical universe
Plato associated one solid with each of the fourbasic elements -- fire, earth, air, and water. Hereserved the fifth for the heavens beyond thestars and planets
Polyhedrons or Polyhedra• A polyhedron is a solid formed by flatsurfaces.• We constructed regular convex polyhedrons:– “regular” refers to the fact that every face, every edgelength, every facial angle, and every dihedral angle (anglebetween two faces) are equal to all the others thatconstitute the polyhedron.– “convex” refers to the fact that all of the sides of theshapes are flat planes, i.e., they are not “concave”, ordented in.
Characteristics of Regular ConvexPolyhedra• Each face is congruent to all others• Each face is regular• Each face meets the others in exactly thesame way
Works CitedEarth Grids http://www.timstouse.com/EarthChanges/earthgrids.htm Web 19 April 2013Ephemeral Curios: Elements of geometryemilyd47.blogspot.com Web 19 April 2013https://docs.google.com/viewer?a=v&q=cache:qtxdpx4mI6gJ:www.lexingtoncatholic.com/faculty/smcgrath/Platonic%2520Solids.ppt+&hl=en&gl=us&pid=bl&srcid=ADGEESh3lry5SdK6isP-BErO4iLrA6gWtrKQ7i_WP6pn5u89LRaDCMqCT9TnG5mFK5S807dj2ql_l6j1iZ_3Wn5lZUWvq0yNWHPuCJ4huUwGid2Rfzx3OWLBvTr_0tCIJmzIIjKYex0P&sig=AHIEtbQ9m7Ap7Yzm81vMFMd2gFjjJuJesQ Web 20 April 2013Platonic solid: Facts, Discussion Forum, and Encyclopedia Articlewww.absoluteastronomy.com Web 19 April 2013Tetrahedron - Wikipedia, the free encyclopediaen.wikipedia.org Web 19 April 2013Orb and the Tetrahedrons [part 5] | THEMZINIthemzini.wordpress.com Web 19 April 2013Icosahedron - Wikipedia, the free encyclopediaen.wikipedia.org Web 19 April 2013File:Dodecahedron.jpg - Wikipedia, the free encyclopediaen.wikipedia.org Web 19 April 2013Ametrinewww.crystalsrocksandgems.com Web 19 April 2013Worlds Biggest Geodesic witchweb.net Web 19 April 2013Una infección recurrente y que no se cura e-consulta.com Web 19 April 2013Petunia Wikimedia Commons commons.wikimedia.org Web 19 April 2013www.overunity.com Web 19 April 2013Lets Study Sacred Geometry www.dreamviews.com