platonic solids in nature

Platonic SolidsSixth Grade Geometry

Cube

Tetrahedron

Octahedron

Icosahedron

Dodecahedron

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.

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

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

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.

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

Five Platonic Solids

Platonic Solids in Nature

PETUNIA

DODECAHEDRON

HERPES VIRUS

Icosahedron

Geodesic dome

Icosahedron

AMETRINE QUARTZ CRYSTAL

ICOSAHEDRON

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 2013

Ephemeral 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 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 2013Una 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