User:Patrick/wallpaper groups

• wallpaper group
• nl:Behangpatroongroep

The region shown is a choice of the possible translation cells with minimum area. The yellow region is a fundamental domain.

Least rotation	Has reflection?
	Yes	No
360° / 6	p6m (*632)	p6 (632)
360° / 4	Has mirrors at 45°? Yes: p4m (*442) No: p4g (4*2)	p4 (442)
360° / 3	Has rotocenter off mirrors? Yes: p31m (3*3) No: p3m1 (*333)	p3 (333)
360° / 2	Has perpendicular reflections? Yes No Has rotocenter off mirrors?     pmg (22*)     Yes: cmm (2*22) No: pmm (*2222)	Has glide reflection? Yes: pgg (22x) No: p2 (2222)
none	Has glide axis off mirrors? Yes: cm (*x) No: pm (**)	Has glide reflection? Yes: pg (xx) No: p1 (o)

• 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