Incommensurate modulations are increasingly being recognized as a common phenomenon in solid-state compounds ranging from inorganic materials to molecular crystals. The origins of such modulations are often mysterious, but appear to be as diverse as the compounds in which they arise. In this Article, we describe the crystal structure and bonding of Co3Al4Si2, the delta phase of the Co-Si-Al system, whose modulated structure can be traced to a central concept of inorganic chemistry: the 18 electron rule. The structure is monoclinic, conforming to the 3 + 1D superspace group C/2m(0 beta 0)s0. The basis of the crystal structure is a rod packing of columns of the fluorite (CaF2) type, a theme that is shared by the recently determined structure of Fe8Al17.4Si7.6. The columns are arranged into sheets, within which the fluorite structure's primitive cubic network of Si/Al atoms continues uninterrupted from column to column. Between the sheets, layers of interstitial Si/Al atoms occur, some of which are arranged with a periodicity incommensurate with that of the fluorite-type columns. Strong modulations in the interstitial layers result. Electronic structure calculations, using a DFT-calibrated Huckel model on a commensurate approximate structure, reveal that the complex pattern of atoms within these interstitial layers serves to distribute Si/Al atoms around the Co atoms in order to reach 18 electron counts (filled octadecets). Central to this bonding scheme is the covalent sharing of electron pairs between Co atoms. The shared electron pairs occupy orbitals that are isolobal to classical Co-Co sigma and pi bonds, but whose stability is tied to multicenter character involving bridging Si/Al atoms. Through these features, Co3Al4Si2 expands the structural and electronic manifestations of the 18 electron rule in solid-state inorganic compounds.