Using GDAL to get vertices of a multipolygon

I am successfully using GDAL to get the vertices of a polygon from a ShapeFile using .NET code. This link showed me how to do that:

http://geoinformaticstutorial.blogspot.com/2012/10/accessing-vertices-from-polygon-with.html

However if the shape type is a multipolygon, then this process does not get any vertices. How can I get the vertices of a multipolygon?