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The region shown is a choice of the possible translation cells with minimum area, except for cm and cmm, where a region of twice that area is shown. The yellow region is a fundamental domain.
Least
rotation |
Has reflection? |
| Yes |
No |
| 360° / 6 |
|
|
| 360° / 4 |
| Has mirrors at 45°? |
| Yes:
|
No:
|
|
|
| 360° / 3 |
| Has rotocenter off mirrors? |
| Yes:
|
No:
|
|
|
| 360° / 2 |
| Has perpendicular reflections? |
| Yes |
No |
| Has rotocenter off mirrors? |
|
Yes:
cmm (2*22) (the rhombus inside is the translation cell)
|
| No:
|
|
| Has glide reflection? |
| Yes:
|
| No:
|
|
| none |
| Has glide axis off mirrors? |
Yes:
cm (*x) (the rhombus inside is the translation cell)
|
No:
|
|
| Has glide reflection? |
| Yes:
|
| No:
|
|
- 5x rhombus 60°
- 2x rhombus, or rectangle in symmetrically staggered rows
- 3x square
- 5x rectangle:
- rectangular grid:
- p2mm double symmetry
- p2m single symmetry
- alternating rows (say hor):
- pg - each other's mirror image with vertical axis
- pmg - each rot-2, each other's mirror image
- pgg - checkerboard pattern, all fields rot-2, with per color in diagonal alternatingly mirror image
- 2x parallelogram
pmg: a10 b10 d01 c01 a10 b10 d01 c01 a00 b00 d11 c11 a00 b00 d11 c11 c00 d00 b11 a11 c00 d00 b11 a11 c10 d10 b01 a01 c10 d10 b01 a01 a10 b10 d01 c01 a10 b10 d01 c01 a00 b00 d11 c11 a00 b00 d11 c11 c00 d00 b11 a11 c00 d00 b11 a11 c10 d10 b01 a01 c10 d10 b01 a01 a b d c a b d c c d b a c d b a a b d c a b d c c d b a c d b a 10 10 01 01 10 10 01 01 00 00 11 11 00 00 11 11 00 00 11 11 00 00 11 11 10 10 01 01 10 10 01 01 10 10 01 01 10 10 01 01 00 00 11 11 00 00 11 11 00 00 11 11 00 00 11 11 10 10 01 01 10 10 01 01
