The free QGIS software can be used to easily convert points in shapefile maps to polygons. The resulting polygon map can be loaded directly into StatPlanet to create an interactive point map, such as an interactive map of world cities or US cities.

Converting points to polygons can be done in just three steps:

1. Insert the points layer: In QGIS, insert the shapefile map containing the points layer, through the menu: Layer -> Add Layer -> Add Vector Layer. Select browse to find the shapefile map file, and select open. It will be added as a layer in the 'Layers' panel on the left-hand side of the screen.
2. Create a buffer around the points: Select from the menu: Vector -> Geoprocessing Tools -> Buffer(s). In the Buffer(s) window, set the Buffer distance, e.g. 0.1 or 1 depending on how large you would like the polygons to be. 
3. Save the point map: In the Buffer(s) window, specify the "Output shapefile" (e.g. "polygons_from_points.shp"). Select OK to save the polygons converted from points to the filename specified.

You can also add a map layer to the points map, for example, to have the country or world map as an outline. This requires you to add a new map layer (as described in step 1) containing the relevant map, and then merge it with the points map layer. See also creating multi-layer shapefile maps for details. Another way of merging maps is to use the MMQGIS plug-in for QGIS. See also - installing and using the MMQGIS plug-in.