17 Wallpaper Groups
-
KEY
180 degree pivot
120 degree pivot
 90 degree pivot
60 degree pivot
Underlying grid
 Reflection axis
Glide Reflection axis
-

 


 

p1
Orbifold: o
Grid
Translation along1st axis
Translation along 2nd axis
Translations llustrated because this has only translational symmetry
p2
Orbifold: 2222
Grid and pivot points
corners
side centers
face centers
-

 


 


 

p3
Orbifold: 333
Grid and pivot points
1st set of corners
2nd set of corners
face centers
p4
Orbifold: 442
Grid and pivot points
  corners
side centers
face centers
p6
Orbifold: 632
Grid and pivot points
corners
side centers
face centers
-

 


 


 


 


 

pm
Orbifold: **
Grid & reflections
1st reflection
2nd reflection
pg
Orbifold: xx
Grid & reflections
1st glide reflection
2nd glide reflection
cm
Orbifold: x*
Grid 
Reflection
Glide Reflection
Reflection
pmm
Orbifold: *2222
Grid
Ref 1    Ref 2
Ref 3    Ref4
1st set corners
2nd set corners
1st Face Center
2nd Face Center
pgg
Orbifold: 22x
Grid
Horizontal Glide Reflection
Vertical Glide Reflection
Side Center
  Face Center
-

 


 


 


 

pmg
Orbifold: 22*
Grid
Reflection
1st Glide Reflection
2nd Glide Reflection
Side Point
cmm
Orbifold: 2*22
Grid
1st Reflection
2nd Reflection
1st Glide Reflection
2nd Glide Reflection
Face Center
Side Point
p4m
Orbifold: *442
Grid
Face
Side
Corner
1st Reflection
2nd Reflection
3rd Reflection
4th Reflection
p4g
Orbifold: 4*2
Grid
Corner
Corner
1st Reflection
2nd Reflection
1st Glide Reflection
2nd Glide Reflection
-
p3m1
Orbifold: *333
Grid
Corner
Face
Face
1st Reflection
2nd Reflection
3rd Reflection
1st Glide Reflection
2nd Glide Reflection
3rd Glide Reflection
p31m
Orbifold: 3*3
Grid
Corner
Corner
1st Reflection
2nd Reflection
3rd Reflection
p6m
Orbifold: *632
Grid
Corner
Face
Side
1st Reflection  2nd Reflection
3rd Reflection  4th Reflection
5th Reflection  6th Reflection
1st Glide Ref  2nd Glide Ref
3rd glide Ref  4th Glide Ref
5th Glide Ref  6th Glide Ref
-
This table is based on G. Polya's illustration of the 17 plane symmetry groups
as pictured on page 23 of Doris Schattschneider's
M. C. Escher - Visions of Symmetry
published by W. H. Freeman & Company.
 -
My Tessellation Coloring Book
A Hop David coloring book of Escher like tessellations.
-
My Geometrical Designs Coloring Book
A Hop David coloring book of various geometrical landscapes.
A lot of pages are devoted to space filling polyhedra with an emphasis on octahedra alternating with tetrahedra.
There's also some polyhedra studies, logarithmic spirals, fractals (only the first few iterations or they'd be impossible to color!) and some miscellaneous.
-
Hop's Escher like tessellations.
Hop's page of Islamic tiles.
Hop's gallery of paintings & drawings.
-
Other pages on the 17 wallpaper groups:
Xah Lee
David Joyce
Andrew Crompton
Japanese Designs