Knotting of contractible two-dimensional polyhedra in $\mathbf R^4$

In this paper the Zeeman conjecture that any piecewise linear embedding of the dunce's hat (i.e. the triangle $ABC$ with the oriented edges $AB$, $BC$, and $AC$ identified) in $\mathbf R^4$ has simply connected complement is disproven.
Indeed, the author constructs linear embeddings in $\mathbf R^4$ with non-simply-connected complements for a class of two-dimensional polyhedra. All of these, just as the dunce's hat, are contractible but not combinatorially contractible, and the author ventures to conjecture that any two-dimensional polyhedra with these properties admits a piecewise linear embedding in $\mathbf R^4$ with non-simply-connected complement.
Figures: 4.
Bibliography: 7 titles.