Modern western square dance of "patter calls" and "singing calls", the two types of square dance calls. The logos shown on the right are the international square dance logo and the modern Alliance of Round, Traditional and Square-Dance logo. Modern western square dancing is a non-competitive activity. There are no dance competitions, and apart from fun events, no prizes are ever offered or sought for 'best dancer' or 'best square'. Particularly at the 'challenge' levels there is large degree of personal satisfaction to be gained from the problem solving element of completing a dance. At all levels the main elements are to enjoy the
Order-4-5 square honeycomb square tiling existing around each vertex in an order-6 square tiling vertex arrangement. It has a second construction as a uniform honeycomb, Schläfli symbol {4,(4,3,4)}, Coxeter diagram, , with alternating types or colors of square tiling cells. In Coxeter notation the half symmetry is [4,4,6,1] = [4,((4,3,4))]. In the geometry of hyperbolic 3-space, the order-4-infinite square honeycomb is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {4,4,∞}. It has infinitely many square tiling, {4,4}, around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many square tiling existing around each vertex in an infinite-order square