9873
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
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.
Contributed by:
Enrique Zeleny
THINGS TO TRY
Automatic Animation
SNAPSHOTS
DETAILS
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)
RELATED LINKS
Group
(
Wolfram
MathWorld
)
Multiplication Table
(
Wolfram
MathWorld
)
Rotation
(
Wolfram
MathWorld
)
Reflection
(
Wolfram
MathWorld
)
Symmetry
(
Wolfram
MathWorld
)
PERMANENT CITATION
"
Group of Symmetries of the Square
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/GroupOfSymmetriesOfTheSquare/
Contributed by:
Enrique Zeleny
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 »
Download Demonstration as CDF »
Download Author Code »
(preview »)
Files require
Wolfram
CDF Player
or
Mathematica
.
Related Demonstrations
More by Author
Crystallographic Point Groups
Enrique Zeleny
Examples of Abelian Groups
Enrique Zeleny
Guessing the Symmetry Group
Izidor Hafner
Generating 3D Figures with a Given Symmetry Group
Izidor Hafner
C3v Group Operations
S. M. Blinder
Symmetries of a Prism
Izidor Hafner
Icosahedral Group Polyhedra
Ed Pegg Jr
Guess the Wallpaper Group
Izidor Hafner
Guessing the Frieze Group
Izidor Hafner
Multiplication Tables for the Group of Integers Modulo n
Jaime Rangel-Mondragon
Related Topics
Group Theory
Browse all topics
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to
Mathematica Player 7EX
I already have
Mathematica Player
or
Mathematica 7+