Dimeric Structure Representation:
$$\text{Solid State: } \text{Layered lattice structure containing octahedral } \text{Al}^{3+} \text{ coordination}$$
$$\text{Vapor/Aprotic Solvent State: } \text{Al}_2\text{Cl}_6 \text{ dimer with } 2 \text{ coordinate-covalent } \text{Al--Cl} \text{ bridge bonds}$$
$$\text{High Temperature (> 1000 K): } \text{Monomeric planar } \text{AlCl}_3 \text{ (sp}^2 \text{ hybridized)}$$
Concept: Anhydrous $$\text{AlCl}_3$$ completes its electron octet by forming a dimer ($$\text{Al}_2\text{Cl}_6$$) via coordinate bonds donated by chlorine atoms to vacant orbitals of aluminium.