A 3-pseudomanifold is a finite connected simplicial 3-complex
K
\mathcal {K}
such that every triangle in
K
\mathcal {K}
belongs to precisely two 3-simplices of
K
\mathcal {K}
, the link of every edge in
K
\mathcal {K}
is a circuit, and the link of every vertex in
K
\mathcal {K}
is a closed 2-manifold. It is proved that for every finite set
∑
\sum
of closed 2-manifolds, there exists a 3-pseudomanifold
K
\mathcal {K}
such that the link of every vertex in
K
\mathcal {K}
is homeomorphic to some
S
∈
∑
S\, \in \,\sum
, and every
S
∈
∑
S\, \in \,\sum
is homeomorphic to the link of some vertex in
K
\mathcal {K}
.