2 * N twists
------------

  4  =  2 twist
  6  =  3 twist
  8  =  4 twist
 16  =  8 twist
 30  = 15 twist
 40  = 20 twist (megaminx) 
  
  7  =  4 corners moved
  9  =  4 corners moved
 17  =  8 corners moved, 27 = 12, 37 = 16, 47 = 20???

 70  =  4 corners moved
 70  =  3 edges moved

110  =  one 5 cycle of edges
210  =  two 5 cycles of edges

20 * N flips
------------

  40  =  2 flip
  80  =  4 flip
 160  =  8 flip
 200  = 10 flip
 240  = 12 flip  (this works for megaminx or 3x3x3)
 280  = 14 flip
 320  = 16 flip
 560  = 28 flip
 600  = 30 flip

other
-----

  40  = double 2 swap

  90  = edge order 4

 600  = superflip-twist (600 can also be superflip)

 500  = 10 spot o5, 12 spot o2,o3... also 3x3x3 spot patterns
 
 517  = midpoint of 10 spot 

 540  = 12 spot + 20 twist
 541  = 10 checkerboard o5, 12 checkerboard o2, o3 rotated
 610  = 10 checkerboard o5 with NO ROTATIONS!

 580  = 12 spot + 4 flip

 610  = 5 spot order 5 shifted twice
 721  = 5 spot order 5

 820 = 12 spot order 2 + 16 flip
1100 = 12 spot order 2 + 30 flip

1110 = 10 stars o5, 12 stars o3, 12 stars o2

3x3x3
-----
  17 = cross patterns

 250 = 6x o6, 6x o3, 6x o2

EDGE/2p 1 (X)1 (1:8 3:4) 3 250 
6 X order 3 pattern