Triangle Tessellation with Hexagonal Gap
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.
This try has rotation points fixed at a third of the distance along the triangle, and another one allows you to set the rotation point.
http://www.geogebratube.org/material/show/id/118940
The gaps are essentially a second tile, since they are all congruent.
More GeoGebra at mathhombre.blogspot.com/p/geogebra.html