Cutting a torus
A solid torus of revolution can be cut by n (> 0) planes into maximally

  
    
      
        
          
            (
            
              
                
                  n
                  +
                  2
                
              
              
                
                  n
                  −
                  1
                
              
            
            )
          
        
        +
        
          
            (
            
              
                
                  n
                
              
              
                
                  n
                  −
                  1
                
              
            
            )
          
        
        =
        
          
            
              1
              6
            
          
        
        (
        
          n
          
            3
          
        
        +
        3
        
          n
          
            2
          
        
        +
        8
        n
        )
      
    
    {\displaystyle {\begin{pmatrix}n+2\\n-1\end{pmatrix}}+{\begin{pmatrix}n\\n-1\end{pmatrix}}={\tfrac {1}{6}}(n^{3}+3n^{2}+8n)}
  parts.The first 11 numbers of parts, for 0 ≤ n ≤ 10 (including the case of n = 0, not covered by the above formulas), are as follows:

1, 2, 6, 13, 24, 40, 62, 91, 128, 174, 230, ... (sequence A003600 in the OEIS).
In the lower doses used for water fluoridation, the only clear adverse effect is dental fluorosis, which can alter the appearance of childrens teeth during tooth development; this is mostly mild and is unlikely to represent any real effect on aesthetic appearance or on public health. A chronic fluoride ingestion of 1 ppm of fluoride in drinking water can cause mottling of the teeth (fluorosis) and an exposure of 1.7 ppm will produce mottling in 30%–50% of patients. Chemical structure
Sodium fluoride is an inorganic ionic compound, dissolving in water to give separated Na+ and F− ions. Like sodium chloride, it crystallizes in a cubic motif where both Na+ and F− occupy octahedral coordination sites; its lattice spacing, approximately 462 pm, is somewhat smaller than that of sodium chloride. Occurrence
The mineral form of NaF, villiaumite, is moderately rare. It is known from plutonic nepheline syenite rocks. Production
NaF is prepared by neutralizing hydrofluoric acid or hexafluorosilicic acid (H2SiF6), both byproducts of the reaction of fluorapatite (Ca5(PO4)3F) from phosphate rock during the production of superphosphate fertilizer. Neutralizing agents include sodium hydroxide and sodium carbonate. Alcohols are sometimes used to precipitate the NaF:

HF  +  NaOH  →   NaF  +  H2OFrom solutions containing HF, sodium fluoride precipitates as the bifluoride salt sodium bifluoride (NaHF2). Heating the latter releases HF and gives NaF. HF  +  NaF  ⇌   NaHF2In a 1986 report, the annual worldwide consumption of NaF was estimated to be several million tonnes. See also
Cryolite
Fluoride therapy

References
External links
"Sodium fluoride".