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# The five platonic solids

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## Joe Bob Brezenski

on 5 April 2013

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#### Transcript of The five platonic solids

Where did the name Platonic come from? These shapes were named after Plato, a Greek Philosopher. Plato did not discover these shapes, but they were still named after him because of the heavy importance he placed on these 5 perfect solids. Why are there only 5? The answer is very simple, because of the angles at the vertices. Math research project The 5 Platonic Solids Sides, Edges, Faces and Vertices A regular triangle has internal angles of 60°, so we can have:
3 triangles (3×60°=180°)
4 triangles (4×60°=240°)
or 5 triangles (5×60°=300°)

A square has internal angles of 90°, so there is only:3 squares (3×90°=270°)

A regular pentagon has internal angles of 108°, so there is only:
3 pentagons (3×108°=324°) The angles at the Vertex have to be less
than 360 degrees Well, why don't some of them work? # of sides each face has # of faces that meet degrees Does it work? 3
3
4
4
5
3
5
4
5
etc... 3
4
3
4
3
5
4
5
5
etc... 180
240
270
360
324
300
432
450
540
etc... (has to be uder 360 degrees) Euler's Formula Euler's Formula says: for any convex polyhedron (which includes the Platonic Solids) the Number of Faces plus the Number of Vertices (corner points) minus the Number of Edges always equals 2. So, does it work? 4+4-6=2 6+8-12=2 20+12-30=2 12+20-30=2 8+6-12=2 As you can see there are only 5 regular Solids that can work. If you disagree, good luck trying to prove it otherwise. :D My Scources
http://www.math.utah.edu/~pa/math/polyhedra/polyhedra.html

http://www.mathsisfun.com/geometry/platonic-solids-why-five.html

http://www.natures-word.com/sacred-geometry/the-platonic-solids/introduction-to-the-platonic-solids