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/19uiDUri76
QRNH_2V_U7vUvuTj87gzXgMKhOp8i8_7NY/vi
ewform

19. Works Cited
Earth Grids http://www.timstouse.com/EarthChanges/earthgrids.htm Web 19 April 2013
Ephemeral Curios: Elements of geometryemilyd47.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 Articlewww.absoluteastronomy.com Web 19 April 2013
Tetrahedron - Wikipedia, the free encyclopediaen.wikipedia.org Web 19 April 2013
Orb and the Tetrahedrons [part 5] | THEMZINIthemzini.wordpress.com Web 19 April 2013
Icosahedron - Wikipedia, the free encyclopediaen.wikipedia.org Web 19 April 2013
File:Dodecahedron.jpg - Wikipedia, the free encyclopediaen.wikipedia.org Web 19 April 2013
Ametrinewww.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 2013Let's Study Sacred Geometry www.dreamviews.com