After learning about Kagome lattices at the New Magnetic Field Frontiers workshop at Ecole Physique des Houches in Les Houches in the French alps, I thought that this shape would adapt well to being a coaster.
The Kagome lattice takes its name from the weave of some baskets which originate in Japan (http://ej.iop.org/images/0953-8984/19/14/140301/kagome.gif). This geometry is used in atomic physics experiments in the form of an optical lattice to trap atoms - imagine putting an atom at each of the vertices of this shape.
I built up the overall coaster in Sketchup from the base unit of a star shape, and this is in turn built up from small triangles.
In V1: This was built up from 3D triangle shapes, which when put together caused all kinds of screwy faces missing, and whilst the .stl file looked okay, the gcode it produced was garbage.
In V2: This was built with 2D triangles, then the entire shape was extruded as a single piece in SketchUp. This not only makes the .stl and gcode output work properly, but also makes it easier to adjust the height of the coaster in SketchUp by using the Push/Pull feature on the top face.
In V3: I added a solid base to V2 in order to catch any condensation which runs off your glass - the previous versions just let this run through, which can make a mess.
At 100% scale, this is around 9.6 cm by 8.3 cm - so it should be printable on even the smallest of 3D printers (e.g. the Printrbot Jr).