Platonic solids in nature

1. Platonic Solids Sixth Grade Geometry

2. Cube

3. Tetrahedron

4. Octahedron

5. Icosahedron

6. Dodecahedron

7. A History of Platonic Solids There are five regular polyhedra that were discovered by the ancient Greeks. The Pythagoreans knew of the tetrahedron, the cube, and the dodecahedron; the mathematician Theaetetus added the octahedron and the icosahedron.

8. These shapes are called the Platonic solids, after the ancient Greek philosopher Plato; Plato, who greatly respected Theaetetus ' work, speculated that these five solids were the shapes of the fundamental components of the physical universe

9. Plato associated one solid with each of the four basic elements -- fire, earth, air, and water. He reserved the fifth for the heavens beyond the stars and planets

10. Polyhedrons or Polyhedra A polyhedron is a solid formed by flat surfaces. We constructed regular convex polyhedrons : “regular” refers to the fact that every face, every edge length, every facial angle, and every dihedral angle (angle between two faces) are equal to all the others that constitute the polyhedron.  “convex” refers to the fact that all of the sides of the shapes are flat planes, i.e., they are not “concave”, or dented in. 

11. Characteristics of Regular Convex Polyhedra Each face is congruent to all others Each face is regular Each face meets the others in exactly the same way    

12. Five Platonic Solids

13. Platonic Solids in Nature

14. PETUNIA DODECAHEDRON

15. HERPES VIRUS Icosahedron

16. Geodesic dome Icosahedron

17. AMETRINE QUARTZ CRYSTAL ICOSAHEDRON

18. Platonic Solid Quiz https://docs.google.com/forms/d/19uiDUri76QRNH_2V_U7vUvuTj87gzXgMKhOp8i8_7NY/viewform

19. Works Cited Earth Grids http://www.timstouse.com/EarthChanges/earthgrids.htm Web 19 April 2013 Ephemeral Curios: Elements of geometry emilyd47.blogspot.com Web 19 April 2013 https://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 2013 Platonic solid: Facts, Discussion Forum, and Encyclopedia Article www.absoluteastronomy.com Web 19 April 2013 Tetrahedron - Wikipedia, the free encyclopedia en.wikipedia.org   Web 19 April 2013 Orb and the Tetrahedrons [part 5] | THEMZINI themzini.wordpress.com   Web 19 April 2013 Icosahedron - Wikipedia, the free encyclopedia en.wikipedia.org Web 19 April 2013 File:Dodecahedron.jpg - Wikipedia, the free encyclopedia en.wikipedia.org Web 19 April 2013 Ametrine www.crystalsrocksandgems.com   Web 19 April 2013 World's Biggest Geodesic witchweb.net Web 19 April 2013 Una infección recurrente y que no se cura e-consulta.com Web 19 April 2013 Petunia  Wikimedia Commons commons.wikimedia.org Web 19 April 2013 www.overunity.com Web 19 April 2013 Let's Study Sacred Geometry www.dreamviews.com