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Only part of world data will appear in ArcMap when the data frame's coordinate system is set to Winkel Tripel.
ArcToolbox' Project wizard for shapefiles and geodatabases will not correctly unproject data from this projection.
The inverse of the Winkel Tripel projection is not working correctly. This is a known issue.
This issue has been addressed in ArcGIS Version 8.1.2.
If you are using ArcGIS 8.1, do one of the following:
A. Click on ArcToolbox button in ArcCatalog to open the ArcToolbox window.
B. Expand Data Management Tools > Projections.
C. Double-click on Project Wizard (shapefiles, geodatabases).