Crystal Lab › The 17 plane groups

The 17 plane groups

2D patterns (wallpaper groups). Open a group to see its symmetry elements drawn in the cell, its operations, and its Wyckoff positions with a model atom you can move.

The 230 space groups · The 17 plane groups · The 7 frieze groups · The 75 rod groups · The 80 layer groups

Oblique (2)

No.	Symbol	Operations	Wyckoff positions	Settings
1	p 1	1	1	1
2	p 2	2	5	1

Rectangular (7)

No.	Symbol	Operations	Wyckoff positions	Settings
3	p 1 m 1	2	3	1
4	p 1 g 1	2	1	1
5	c 1 m 1	4	2	1
6	p 2 m m	4	9	1
7	p 2 m g	4	4	1
8	p 2 g g	4	3	1
9	c 2 m m	8	6	1

Square (3)

No.	Symbol	Operations	Wyckoff positions	Settings
10	p 4	4	4	1
11	p 4 m m	8	7	1
12	p 4 g m	8	4	1

Hexagonal (5)

No.	Symbol	Operations	Wyckoff positions	Settings
13	p 3	3	4	1
14	p 3 m 1	6	5	1
15	p 3 1 m	6	4	1
16	p 6	6	4	1
17	p 6 m m	12	6	1

Operations are counted per conventional cell (lattice centring included). Symbols follow the International Tables; the first listed setting is the standard one.