Triangle Tessellation with Gaps
We were working on Islamic tessellations in class, and Ashley Short came up with a nice one, that had several different structures.
http://ashleynshort.weebly.com/mth-495-spring-2014/tessellations#comments
That was enough to get me experimenting with intentionally leaving a gap.
So my first try has rotation points fixed at a third of the distance along the triangle (http://www.geogebratube.org/material/show/id/118949), and this one allows you to set the rotation point. So this could be a simple midpoint rotation tessellation of an equilateral triangle, or you can get funky.
More GeoGebra at mathhombre.blogspot.com/p/geogebra.html