  We show that minimally 3-rigid block-and-hole graphs, with one block or one
hole, are characterised as those which are constructible from $K_3$ by vertex
splitting, and also, as those having associated looped face graphs which are
$(3,0)$-tight. This latter property can be verified in polynomial time by a
form of pebble game algorithm. We also indicate connections to the rigidity
properties of polyhedral surfaces known as origami and to graph rigidity in
$\ell_p^3$ for $p\not=2$.
