# All minimus extents

There are 10792 extents of minimus. If rotations, reversals and mirror images are discounted, the number drops to 162. The extents may be classified by their symmetry group as follows:
• Number of parts (1, 2, 3 or 4)
• Palindromic symmetry (P) (reflection about a horizontal axis)
• Double symmetry (D) (rotation through 180 degrees)
• Left-right glide reflection symmetry (R)
A method may have zero, one or all three (but not two) of P, D and R symmetries.

The numbers of extents by symmetry group are:

 1 2 3 4 Total none 75 2 0 0 77 P 53 3 4 2 62 D 10 1 0 0 11 R 2 0 0 0 2 PDR 7 0 3 0 10 Total 147 6 7 2 162
Here are the extents arranged by symmetry group.

The number of extents is reduced even further if one ignores "trivial variations" involving Kent or Oxford places. Thus, the place notation fragments x12x and 34.12.34 may always be used interchangeably, and similarly for the pairs x34x, 12.34.12 and 34.12.34, 12.34.12. Taking this into account, there are only 29 essentially different extents, given here in a format emphasising the symmetries.