Semi-regular tessellations

Extract

A semi-regular tessellation is one consisting of regular polygons of the same length of side, with the same ‘behaviour’ at each vertex. By this we mean that the polygons appear in the same order (though different senses are allowed) at each vertex. The three regular tessellations are for convenience included here as special cases of semi-regular ones. An example of a semi-regular tessellation is that with triangle–triangle–square–triangle–square in cyclic order, at each vertex. A shorthand notation (‘Schläfli symbol’) for this is 3.3.4.3.4.