Some images from

 Algebra: Abstract and Concrete

2nd edition

 Frederick M. Goodman

Images from symmetric dynamical systems:

The following images were created using algorithms from Michael Field and Martin Golubitsky, Symmetry in Chaos, Oxford University Press, 1992.

To create the images, one runs several million iterations of a two dimensional discrete dynamical system. The probability density for the location of the dynamical particle is encoded in colors. The dynamical system is chaotic, but possesses inherent symmetry.

For more information, and many more examples, of images created in this manner, follow this link to

Martin Golubitsky's home page.

Symmetry axes of regular polyhedra:

The following are color versions of 2-dimensional images from the text. To see dynamic 3-dimensional images, follow this link.




Duality of regular polyhedra:







Some imbeddings of regular polyhdra:


Tetrahedra in the cube:

tetrahedron in cube

two tetrahedra in cube

Cube in the dodecahedron:

cube in dodecahedron 1

cube in dodecahedron 2