Summary: This paper continues earlier work on mathematical techniques for generating optimized algorithms for computing finite element stiffness matrices. These techniques start from representing the stiffness matrix for an affine element as a collection of contractions between reference tensors and an element-dependent geometry tensor. We go beyond the complexity-reducing binary relations explored by R. C. Kirby, A. Logg, L. R. Scott and A. R. Terrel [SIAM J. Sci. Comput. 28, No. 1, 224–240 (2006; Zbl 1104.65324)] to consider geometric relationships between three or more objects. Algorithms based on these relationships often have even fewer operations than those based on complexity-reducing relations.