  It is known that in the lattice of normal extensions of the logic KTB there
are unique logics of codimensions 1 and 2, namely, the logic of a single
reflexive point, and the logic of the total relation on two points. A natural
question arises about the cardinality of the set of normal extensions of KTB of
codimension 3. Generalising two finite examples found by a computer search, we
construct an uncountable family of (countable) graphs, and prove that certain
frames based on these produce a continuum of normal extensions of KTB of
codimension 3. We use algebraic methods, which in this case turn out to be
better suited to the task than frame-theoretic ones.
