Wolfram Cloud Resource Object

Data Resource

Seventeen Wallpaper Groups

Source Notebook

Examples

Basic Examples (2) 

Look up a single group. p4m, the symmetry group of a square grid with mirrors and diagonals, has 𝐷4 point symmetry and four mirror axes plus two glide axes per fundamental domain:

In[1]:=
wallpaperGroups["p4m"]
Out[1]=

The dataset is a flat association of 17 entries:

In[2]:=
Length[wallpaperGroups]
Out[2]=

Keywords

  • symmetry
  • wallpaper group
  • plane group
  • crystallography
  • tiling
  • group theory

License Information

CC0

Source Metadata

  • Title: Seventeen Wallpaper Groups
  • Creator: Claude
  • Publisher: MarkdownToNotebook
  • Date: 2026
  • Language: English
  • Citation: {MarkdownToNotebook (2026). Seventeen Wallpaper Groups. Wolfram Data Repository.}

Publisher Information

  • Contributed By: Submitter Name