<<Tessellate.m

tri = TriFromAngles[Pi/6,Pi/6,Pi/6];
triangles = N[Table[Map[RotatePoint[#,i*Pi/3]&,tri],{i,0,5}]];

trigroup = Map[PolygonInvGroup[#,1]&,triangles];

$DisplayFunction = Identity;

graf1 = DrawCirclesAroundPolygons[trigroup, Colored -> True];
graf2 = DrawHypPolygons[trigroup, Colored -> True];

$DisplayFunction = Display[$Display, #1]&;

graf = Show[graf1, graf2];

