The Number of Periodic Color Symmetry Groups

Group

Number of colors

 

2

3

4

5

6

7

8

p1

1

1

2

1

1

1

2

p2

2

1

3

1

2

1

4

pm

5

2

10

2

11

2

16

pmm

5

1

13

1

9

1

21

pg

2

2

4

2

5

2

7

pgg

2

1

11

2

11

2

19

pmg

5

2

11

2

11

2

19

cm

3

2

7

2

7

2

13

cmm

5

1

11

1

8

1

21

p4

2

0

5

1

2

0

9

p4m

5

0

13

0

2

0

28

p4g

3

0

7

0

2

0

13

p3

0

2

1

0

1

1

0

p3m1

1

2

1

0

4

0

1

p31m

1

2

1

0

5

0

1

p6

1

2

1

0

5

1

1

p6m

3

2

2

0

11

0

3

Total

46

23

96

14

90

15

166

The table above gives the number of color groups with n colors, for values of n from 2 to 8.  In each row of the table
is the number of groups for a given wallpaper group as the group of the underlying (uncolored) pattern.  You can click on some
of the numbers to see examples.

The calculations in this table were originally published by T. W. Wieting in The Mathematical Theory of Plane Chromatic
Ornament
, Marcel Dekker, 1981.  The table was also reprinted (with more than I have reproduced here) in
Grunbaum and Shephard's Tilings and Patterns.

Color Tiling