A frieze is a pattern that is repeated horizontally, and in addition to such horizontal repetition, a frieze may have additional symmetric properties based on symmetries: the frieze may look the same if it is mirrored vertically, mirrored horizontally, rotated 180 degrees around appropriately chosen points, and finally shifted left or right and then vetrically reflected. Some symmetric properties are shared, for if a pattern can be reflected horizontally, it can also be shifted and then reflected. 

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The most common aid memoires to remember the seven patterns include Λ and Γ, but becomes more frustrating because it also simultaneously includes both Λ and L. This switching between arbitrarily chosen letters from two different alphabets is frustrating. Additionally, there is no rhyme or reason for choosing "H" as opposed to "I", "O" or "X". could almost argue that the letter chosen was the first such letter in the alphabet, but then the letter "N" should be used instead of "S".

 

Instead, I use only those lower case letters comprised of a circle and a stem, including abdopq. No other lower-case letters have this property, so it is simple to recall them. Here are the seven symmetry patterns:

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     o     oooooooo      HHHHH       IOX

     a     aaaaaaaa     BBBBBBBB   CDEK

    bb    bbbbbbbb     FFFFFFFF     GJLPQR

    bd    bdbdbdbd     ΛΛΛΛΛΛΛ     AMTUVWY

    bp    bpbpbpbp     LΓLΓLΓLΓ       

    bq    bqbqbqbq     SSSSSSSSS   NZ

  bdpq  pqbdpqbd     ΛVΛVΛVΛ

 

Note that for ease of memory, the third through sixth patterns are the letter b followed by one of the long-stemmed letters:  bdpq

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What is nicest about the last pattern is that bdpq includes the four long-stemmed letters in the order in which they appear in the alphabet.

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Just to go into detail, all allow a horizontal shift, but also:

1. oooooo allows a vertical reflection (and therefore trivially a horizontal shift followed by a vertical reflection), a horizontal reflection and a rotation.

2. aaaaaa allows a vertical reflection (and therefore trivially a horizontal shift followed by a vertical reflection).

3. bbbbbb allows no other symmetries.

4. bdbdbd allows a horizontal reflection.

5. bpbpbp allows a horizontal shift followed by a vertical reflection (but not just a simple vertical reflection).

6. bqbqbq allows a rotation.

7. qbdpqb allows a horizontal reflection, a horizontal shift followed by a vertical reflection(but not just a simple vertical reflection), and a rotation.