Two common arguments are given below. Both of these arguments only show that there can be no more than five Platonic solids. That all five actually exist is a separate question—one that can be answered by an explicit construction.
Source: Wikipedia > Platonic Solid
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- Platonic solid - Wikipedia, the free encyclopedia, Modified November 25, 2008, 12:00 am
- Platonic Solids, Modified February 27, 2002, 12:00 am
- Platonic Solids, Modified July 11, 2008, 12:00 am
- The Platonic Solids, Modified November 24, 2008, 12:00 am
- Platonic Solids, Modified April 29, 2005, 12:00 am
- Platonic Solids, Modified June 7, 2002, 12:00 am
- Platonic Solids, Modified May 14, 2007, 12:00 am
- The Platonic Solids, Modified September 17, 2006, 12:00 am
- Platonic Solids, Modified February 7, 2005, 12:00 am
- Pythagoras and the five regular Platonic solids., Modified October 18, 2006, 12:00 am