My less-than-perfect drawings provided visuals.
Each student built several shapes using toothpicks and jelly beans. I explained that the jelly beans represented vertices (points where two edges intersect) and the toothpicks represented edges (line segments where two faces intersect). Faces could be determined by holding an index card against a two-dimensional side.
Hint: Use round toothpicks. They don't break as easily.
Their exploration of each shape was recorded on a sheet like this:
It was a simple, one-day activity that provided lots of learning and some fun along the way.