The Great Search for the Platonic Solids

Introduction

          Welcome to the New-Age Order of Pythagoras: The Mathematikoi Society.  To be a member of this society, you must complete a series of events.  These events will challenge you on many different aspects of mathematics.  This is the first of such challenges. 

          Shapes and figures can relate many mathematical topics in a visual form.  They can be thought of as two dimensional or three dimensional.  Three dimensional shapes are better seen created rather than as a drawing.  This way the learner can explore all the faces, edges, and vertices of the shape.  They are easily counted this way. 
          In the two dimensional and three dimensional worlds, shapes can be considered regular.  A shape being regular means that it is the same any way you look at it.  The regular three dimensional shapes are known as the Platonic Solids. 
bullet  What are the Platonic Solids?
bullet  How many Platonic Solids are there? 
bullet  Why is there a limit to the possible number of Platonic Solids?

          These are the questions you will answering in this WebQuest.