Sufficient conditions are given for the existence of open mappings from a p. 1. manifold
M
m
,
m
⩾
3
{M^m},m \geqslant 3
, onto a polyhedron
Q
Q
. In addition, it is shown that a mapping
f
f
from
M
m
,
m
⩾
3
{M^m},m \geqslant 3
, to
Q
Q
is homotopic to a monotone mapping of
M
M
onto
Q
Q
iff
f
∗
:
π
1
(
M
)
→
π
1
(
Q
)
{f_ \ast }:{\pi _1}(M) \to {\pi _1}(Q)
is onto. Finally, it is shown that a monotone mapping of
M
m
,
m
⩾
3
{M^m},m \geqslant 3
, onto
Q
Q
can be approximated by a monotone open mapping of
M
M
onto
Q
Q
.