Converting a curve to a mesh

I’m importing an SVG file into Blender, and trying to convert it to a mesh. The imported curve is a closed polygon. I select the curve and, from the Object menu, select “Convert to” and then “Mesh from Curve/Meta/Surf/Text”.

However, the resulting mesh appears to be a rasterized version of my shape. That is, instead of each vertex along the path being connected to its neighbor, it appears that edges are created linking each vertex with a corresponding vertex on the other side of the same.

Why is it doing this? And how do I get the desired behavior?

Have you tried switch to 3D curve type before converting to mesh?