a) Consider a regular triangle $\triangle ABC$, denote its midpoints by $M, N, K$ respectively. (fig. 04). The segments $AN$, $BK$ and $CM$ intersect at $O$. It is easy to see that the quadrilaterals $BMON$, $CKON$ and $AMOK$ satisfy the condition.

b) Now let us denote the midpoints of $OM$, $ON$ and $OK$ by $P$, $R$ and $Q$ respectively. The pentagons which we are looking for are $ABROP$, $ROQCB$ and $APOQC$.