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Platonic SolidsSixth Grade Geometry
Cube
Tetrahedron
Octahedron
Icosahedron
Dodecahedron
A History of Platonic Solids• There are five regular polyhedra that werediscovered by the ancient Greeks.• The Pythagorean...
These shapes are called the Platonic solids,after the ancient Greek philosopher Plato;Plato, who greatly respected Theaete...
Plato associated one solid with each of the fourbasic elements -- fire, earth, air, and water. Hereserved the fifth for th...
Polyhedrons or Polyhedra• A polyhedron is a solid formed by flatsurfaces.• We constructed regular convex polyhedrons:– “re...
Characteristics of Regular ConvexPolyhedra• Each face is congruent to all others• Each face is regular• Each face meets th...
Five Platonic Solids
Platonic Solids in Nature
PETUNIADODECAHEDRON
HERPES VIRUSIcosahedron
Geodesic domeIcosahedron
AMETRINE QUARTZCRYSTALICOSAHEDRON
Platonic Solid Quiz• https://docs.google.com/forms/d/19uiDUri76QRNH_2V_U7vUvuTj87gzXgMKhOp8i8_7NY/viewform
Works CitedEarth Grids http://www.timstouse.com/EarthChanges/earthgrids.htm Web 19 April 2013Ephemeral Curios: Elements of...
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Platonic solids in nature

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Platonic solids in nature

  1. 1. Platonic SolidsSixth Grade Geometry
  2. 2. Cube
  3. 3. Tetrahedron
  4. 4. Octahedron
  5. 5. Icosahedron
  6. 6. Dodecahedron
  7. 7. 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.
  8. 8. 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
  9. 9. 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
  10. 10. 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.
  11. 11. Characteristics of Regular ConvexPolyhedra• Each face is congruent to all others• Each face is regular• Each face meets the others in exactly thesame way
  12. 12. Five Platonic Solids
  13. 13. Platonic Solids in Nature
  14. 14. PETUNIADODECAHEDRON
  15. 15. HERPES VIRUSIcosahedron
  16. 16. Geodesic domeIcosahedron
  17. 17. AMETRINE QUARTZCRYSTALICOSAHEDRON
  18. 18. Platonic Solid Quiz• https://docs.google.com/forms/d/19uiDUri76QRNH_2V_U7vUvuTj87gzXgMKhOp8i8_7NY/viewform
  19. 19. 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

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