Because of this, the reverse of any number that is divisible by three (or indeed, any permutation of its digits) is also divisible by three. For instance, 1368 and its reverse 8631 are both divisible by three (and so are 1386, 3168, 3186, 3618, etc.). See also Divisibility rule. This works in base 10 and in any positional numeral system whose base divided by three leaves a remainder of one (bases 4, 7, 10, etc.). Three of the five Platonic solids have triangular faces – the tetrahedron, the octahedron, and the icosahedron. Also, three of the five Platonic solids have vertices where three faces meet – the tetrahedron, the hexahedron (cube), and the dodecahedron. Furthermore, only three different types of polygons comprise the faces of the five Platonic solids – the triangle, the square, and the pentagon. There are only three distinct 4×4 panmagic squares. According to Pythagoras and the Pythagorean school, the number 3, which they called triad, is the noblest of all digits, as it is the only number to equal the sum of all the terms below it, and the only number whose sum with those below equals the product of them and itself.There are three finite convex uniform polytope groups in three dimensions, aside from the infinite families of prisms and antiprisms: the tetrahedral group, the octahedral group, and the icosahedral group.
Three is the only prime which is one less than a perfect square. Any other number which is 
  
    
      
        
          n
          
            2
          
        
      
    
    {\displaystyle n^{2}}
   − 1 for some integer 
  
    
      
        n
      
    
    {\displaystyle n}
   is not prime, since it is (
  
    
      
        n
      
    
    {\displaystyle n}
   − 1)(
  
    
      
        n
      
    
    {\displaystyle n}
   + 1).