Abstract
We implement an algorithm
RSHT (random simple-homotopy)
to study the simple-homotopy types of simplicial complexes, with a particular focus on contractible spaces and on finding substructures in higher-dimensional complexes. The algorithm combines elementary simplicial collapses with
pure elementary expansions
. For triangulated
d
-manifolds with
d
≤
6
, we show that RSHT reduces to (random) bistellar flips. Among the many examples on which we test RSHT, we describe an explicit 15-vertex triangulation of the Abalone, and more generally,
(
14
k
+
1
)
-vertex triangulations of a new series of Bing’s houses with
k
rooms,
k
≥
3
, which all can be deformed to a point using only six pure elementary expansions.