Laves (isohedral tilings)	Duals (Archimedian tilings)
3-3-3-3-3-3	3-3-3-3-3-3
3-3-3-3-6	3-3-3-3-6
3-3-3-4-4	3-3-3-4-4
3-3-4-3-4	3-3-4-3-4
3-4-6-4	3-4-6-4
3-6-3-6	3-6-3-6
3-12-12	3-12-12
4-4-4-4	4-4-4-4
4-6-12	4-6-12
4-8-8	4-8-8
6-6-6	6-6-6

These images taken from the SIGGRAPH 2000 coursenotes for subdivision. http://mrl.nyu.edu/publications/subdiv-course2000/

I have posted these simply because I find them quite interesting. The numbers of the tilings indicate the count of edges entering a vertex for each vertex around a polygon in the Lave. Note that in the lave every tile is the same shape, however this is not true in the Duals. 

The duals are created by placing a vertex in the center of every tile and connecting them.

Some links that were relevant on Sunday October 14th 2001:

• http://www.tilings.org
• http://www.ics.uci.edu/~eppstein/junkyard/tiling.html
• http://people.hws.edu/mitchell/tilings/Part1.html
• go search for MC Escher or Tilings at google.com