The {\em solitaire cone} $S_B$ is the cone of all feasible fractional Solitaire Peg games.
Valid inequalities over this cone, known as pagoda functions, were used to show
the infeasibility of various peg games. The link with the well studied dual metric
cone and the similarities between their combinatorial structures leads
to the study of a dual cut cone analogue; that is, the cone generated by the
$\{0,1\}$-valued facets of the solitaire cone. This cone is called {\it boolean solitaire
cone} and denoted ${\cal B}S_B$. We give some results and conjectures on the combinatorial
and geometric properties of the boolean solitaire cone. In particular we prove that the
extreme rays of $S_B$ are extreme rays of ${\cal B}S_B$ strengthening the analogy with
the dual metric cone which extreme rays are extreme rays of the dual cut cone. Other
related cones are also considered.