PLATONIC SOLIDS

    

      Take 4 pieces of triangle shape.  Join and make a closed form.  You get a prism or pyramid form.  It has some properties.

1.  All the faces are triangle (same polygon)
2. Three triangle meet at every corner.  (same number of polygon meet at each vertex)
3. At each vertex, the three internal angles[angle between sides] are 60+60+60=180 degree.  It is always less than 360 degree.
4. They always satisfy Euler's formula
No. of faces+No. of vertices- No. of edges = 2
   4               +   4                - 6                       =2
This shape is called tetrahedron.  It belongs to platonic solids, named after philosapher plato.  Platonic solids have  the above properties.  There are only five platonic solids in our three dimensional world.

1. Tetrahedron:  3 triangles meet at every corner.
2. Octahedron:  4 triangles meet at every vertex.
3. icosahedron:  5 triangles meet
4. Cube:  3 squares meet
5. dodecahedron:  3 pentagons meet.
      Platonic solid forms are found in many crystal structures.  Many viruses have the shape of icosahedron.  Because it saves space, and they can be built repeatedly  using basic protein units.  Carbon football molecule(fulleene) is in the shape of icosahedron.

     Fair dice are made using platonic solid forms.  Also Rubik's cube come in all five shapes.

     Note:  In four dimensional world, there are six platonic solids.  In dimensions higher than four, only three platonic solids can exist.  Explore.

     Once kepler modelled our solar system based on platonic forms.

    Tetrahedron is something special.  Everybody knows the glass prism splits the white light into spectrum of colours.  Pyramids were built 4500 years ago.  People are still attributing mystic meanings to it.  Prism is used in many optical instruments like telescope and camera.  In tall buildings, mostly this tetrahedron structure is followed.