Platonic Solid Relationships Pt.1
Nate | December 17, 2010
The 5 platonic solids are the known solutions to the problem asking how to make a 3-d shape in a sphere where all vertexes touch the circumference/surface of the sphere and where all the edges have the same length.
Each of the 5 platonic solids has a “dual” which is created by connecting the centers of all the faces together. For example, the cube has 6 faces, and when you connect the centers you get the octahedron which has 6 vertexes. The icosahedron’s dual is the dodecahedron and visa versa. The tetrahedron is it’s own dual so it is called self-dual. You can also get the duals of each shape by truncating them (cutting off all the pointy parts equally). Here are some pictures of some examples:












