A common (hexagonal) tesselation.
Step-by step construction using elementary geometry.
e.g. I have not used of the "Rotate" command, or defined any fixed angles.
Worksheet 1 of at least 4
* 1. Elementary construction.
2. Identify constraints. [url]http://www.geogebratube.org/material/show/id/29316[/url]
3. Redefine the problem.
4. New Questions.
The worksheet references the construction of an equilateral triangle in a circle:
http://www.geogebratube.org/student/m29226
These are self-study materials. Please drop me a line if I can make them more useful for you.