Group of Symmetries of the Square

The table shows the group of symmetries of a square. Two operations of the group are applied successively to the colored squares. Their product is shown in the table.



  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


The operations are defined as follows:
= identity
= rotation 90° clockwise about the center
= rotation 180° clockwise around
= rotation 270° clockwise around
= reflection through the horizontal center line
= reflection through the vertical center line
= reflection through the main diagonal (upper-left to bottom-right vertex)
= reflection through the other diagonal (bottom-left to upper-right vertex)
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.