We start by presenting a brief overview of the various known lattice representations.  From there we introduce some results of our work on TiRS graphs which abstract the lattice duals in Ploscica's representation (1995) via maximal partial maps into the two-element set. Those particular graphs are in a one-to-one correspondence with the elements of a particular subclass of the class of RS frames introduced by Gehrke (2006) to represent perfect lattices.  We show that the canonical extensions of lattices are more than perfect - they are perfect lattices satisfying an extra condition. Although being more than perfect, they are not perfect enough...

This is a joint work with Andrew P.K. Craig (Johannesburg, South Africa) and Miroslav Haviar (Matej-Bel Univ., Slovakia).