While the central theme of the seven chapters has been the interplay of geometry with algebra, another theme, purely algebraic, also ran through the book. Time and time again we have used mappings from one structure to another to simplify a problem.

In Chapters 1 and 2, where we faced an infinite lattice*L*imbedded in a rational lattice*L'*, we formed the quotient group*L'/L.*The natural homomorphism from*L'*to*L'/L*enabled us to work in*L'/L,*which is a finite group, instead of an infinite group.

At the end of Chapter 2 the solution of a brick-tiling

EP - 188 ET - 1 PB - Mathematical Association of America PY - 1994 SN - 9780883850411 SP - 187 T2 - Algebra and Tiling T3 - Homomorphisms in the Service of Geometry UR - http://www.jstor.org/stable/10.4169/j.ctt5hh7z6.11 VL - 25 Y2 - 2021/09/17/ ER -