text: The simplest liquid crystalline phase that is formed by spherical micelles is the micellar cubic, denoted by the symbol I. This is a highly viscous, optically isotropic phase in which the micelles are arranged on a cubic lattice. Prior to becoming macroscopic liquid crystals, tactoids are formed, which are liquid crystal microdomains in an isotrophic phase. At higher amphiphile concentrations the micelles fuse to form cylindrical aggregates of indefinite length, and these cylinders are arranged on a long-ranged hexagonal lattice. This lyotropic liquid crystalline phase is known as the hexagonal phase, or more specifically the normal topology hexagonal phase and is generally denoted by the symbol H.
  At higher concentrations of amphiphile the lamellar phase is formed. This phase is denoted by the symbol L and can be considered the lyotropic equivalent of a smectic A mesophase. This phase consists of amphiphilic molecules arranged in bilayer sheets separated by layers of water. Each bilayer is a prototype of the arrangement of lipids in cell membranes.
  For most amphiphiles that consist of a single hydrocarbon chain, one or more phases having complex architectures are formed at concentrations that are intermediate between those required to form a hexagonal phase and those that lead to the formation of a lamellar phase. Often this intermediate phase is a bicontinuous cubic phase.
  Increasing the amphiphile concentration beyond the point where lamellar phases are formed would lead to the formation of the inverse topology lyotropic phases, namely the inverse cubic phases, the inverse hexagonal columnar phase (columns of water encapsulated by amphiphiles, (H) and the inverse micellar cubic phase (a bulk liquid crystal sample with spherical water cavities). In practice inverse topology phases are more readily formed by amphiphiles that have at least two hydrocarbon chains attached to a headgroup. The most abundant phospholipids that are found in cell membranes of mammalian cells are examples of amphiphiles that readily form inverse topology lyotropic phases.
  Even within the same phases, self-assembled structures are tunable by the concentration: For example, in lamellar phases, the layer distances increase with the solvent volume. Since lyotropic liquid crystals rely on a subtle balance of intermolecular interactions, it is more difficult to analyze their structures and properties than those of thermotropic liquid crystals.
  The objects created by the amphiphiles are usually spherical (as in the case of micelles), but may also be disc-like (bicelles), rod-like, or biaxial (all three micelle axes are distinct). These anisotropic self-assembled nano-structures can then order themselves in much the same way as thermotropic liquid crystals do, forming large-scale versions of all the thermotropic phases (such as a nematic phase of rod-shaped micelles).