  We introduce topological prismatoids, a combinatorial abstraction of the
(geometric) prismatoids recently introduced by the second author to construct
counter-examples to the Hirsch conjecture. We show that the `strong $d$-step
Theorem' that allows to construct such large-diameter polytopes from
`non-$d$-step' prismatoids still works at this combinatorial level. Then, using
metaheuristic methods on the flip graph, we construct four combinatorially
different non-$d$-step $4$-dimensional topological prismatoids with $14$
vertices. This implies the existence of $8$-dimensional spheres with $18$
vertices whose combinatorial diameter exceeds the Hirsch bound. These examples
are smaller that the previously known examples by Mani and Walkup in 1980 ($24$
vertices, dimension $11$).
  Our non-Hirsch spheres are shellable but we do not know whether they are
realizable as polytopes.
