Dedicated to Professor Jack D. Dunitz, who thinks more deeply about structure than anyone else we know There are more than 2000 compounds with RE/M/E 1 : 1 : 1 stoichiometry, where RE is a rare earth, actinide, or from groups 1 ± 4, E is a late transition metal from groups 8 ± 12, and E belongs to groups 13 ± 15. In the first paper of a series, we describe the primary structural characteristics of this large class of compounds, focusing on the geometries and bonding in the [ME] nÀ anionic sublattices. We start with a detailed description of the EuAuSn lattice, by emphasizing its essential building blocks and the symmetry operations connecting them, in order to set up a way of describing systematically the geometric features of other RE M E frameworks. Nearly all these phases have eclipsed hexagonal layered arrangements (with only MÀE bonds within these slabs) in the ME sublattice. In most cases, stacking the puckered layers in the third dimension gives rise to MÀE, MÀM, or EÀE bonds, alternating in certain patterns. We point to several interesting sets of RE M E compounds, of like structure, but whose electron counts vary significantly. The structures of nonlayered networks and their mostcommon electron counts are also introduced.Enumeration. ± In this work, we begin to look at bonding patterns in a large group of ternary compounds with the RE/M/E 1 : 1 : 1 stoichiometry, where RE rare earth (lanthanide (Ln) or actinide (An)), alkali, alkaline earth, or from groups 3 and 4, M late transition metal, from groups 8 ± 12, and E main group element, from groups 13 ± 15. In the periodic table in Fig. 1, we highlighted with yellow the elements we refer to as RE, M in red, and E in blue. We will call the general class the RE M E structures. In CRYSTMET (a database for inorganic compounds) [1] and ICSD (Inorganic Crystal Structure Database) [2], more than 2000 substances fall into this category.As shown in Table 1, more than 60% of compounds have a lanthanide (Ln) as countercation. This is the reason for our use of RE in the RE M E class notation, albeit many phases do not contain a lanthanide. In Tables 2 and 3 from Appendix, we list the compounds, grouping them (somewhat arbitrarily) by the space groups in which they crystallize, and give the archetypical structure types, along with simple descriptions of their structural characteristics and electron counts. We are going to refer to these tables throughout our subsequent discussion.We abbreviate orthorhombic-RE M E as o-RE M E, hexagonal-RE M E as h-RE M E, cubic-RE M E as c-RE M E, tetragonal-RE M E as t4-RE M E, trigonal-RE M E as t3-RE M E, and monoclinic-RE M E as m-RE M E.As may be seen from Table 1, there is ± to put it mildly ± a myriad of RE M E phases, covering most but not all possibilities. Fig. 5.[AuGe] 2À Sublattice of EuAuGe. On the left side is given the layer sequence, and, on the right, the corresponding bond notation.