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The five platonic solids
Transcript of The five platonic solids
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
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
Google images Thanks for watching!