# Symmetry

56 57 Appendix Groups 56 POINTGROUPS 2d symmetry about a centre, with rotation around a centre left reflection about a line middle and reflection plus rotation right. LINEGROUPS 2d symmetry along a line. The combination of the operations of repetition, rotation and reflection about a line produce seven line groups that may, in theory, extend to infinity right NETS The five basic nets below are the grids on which the variations of plane patterns are constructed PLANE GROUPS In creating plane patterns from a given motif we encounter a similar set of rules which similarly lead to a range of creative possibilities. Using the basic nets, a motif may be moved through every combination of rotation and reflection to produce precisely seventeen configurations below PLANE DIVISION Similar constraints govern the regular divisiontiling of the plane. It is the case that there are only three ways to do this using regular polygons. Those with three, four and six sides the square, equilateral triangle hexagon will fill the plane by themselves, but fivesiders pentagons will not and this is simply the peak of a hierarchy of planedivision classification. As well as the three regular divisions 13, there are eight semiregular grids 411, and fourteen demi regular grids 1225, which together make up all the variations using regular polygons. 57 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25