Or maybe something like this...
poly = {
10, 5,
15, 20,
5, 10,
0, 0
} // Partition[#, 2] &
i = 0;
Graphics[
{
FaceForm[None]
, EdgeForm[{GrayLevel[0.7], Thickness[Large]}]
, poly // Polygon
, PointSize[Large]
, Black
, Point[poly]
, Map[Style[Text[++i, #, {-2, -1}], Red, Large, Bold] &, poly]
}
, Frame -> True
]
