In Wikipedia
a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides.
Wouldn't it be enough just to say "a parallelogram is a quadrilateral with two pairs of parallel sides", i.e. that this automatically implies that the quadrilateral is simple if it has two pairs of parallel sides.
You may suppose that we consider parallelograms in 3D space (simply vector geometry);
Other sources require that it is convex and lies in a plane (for example the German version of Wikipedia):
Ein Parallelogramm [...] ist ein konvexes ebenes Viereck, bei dem gegenüberliegende Seiten parallel sind.
In English:
"A parallelogram is a convex plane quadrilateral, where two opposite sites are parallel"
Same question here: May we omit "convex" "plane" and "opposite" in the sense that it leads to the same type of object.