There are 2 types of types in metadata! 🙂 I tend to refer to them as model types and public types. As an example the 3 public types Dashboard, Indicator, Range all have the same model type of Transformation. Using the metadata API you would query Transformation objects to find them, and you would filter on the PublicType attribute to narrow it down to objects with the public type you are after. Public types have type-names as well as labels e.g. "Information Map (Relational)" has a TypeName of "InformationMap.Relational". From the examples in the relationship reporting tools doc it looks like you need to use the public type's TypeName for -types e.g. InformationMap, InformationMap.Relational, Dashboard, Indicator, Range, StoredProcess, Report.StoredProcess etc.
The metadata server includes metadata about this public type metadata under /System/Types 🙂 We do lots of metadata querying at Metacoda so we built some tools to help us find what we need. There are 2 free ones that you might find useful here: the 1) Public Types Explorer plug-in makes public type metadata easier to browse - see http://www.metacoda.com/en/products/utility-plug-ins/public-types-explorer/ and http://platformadmin.com/blogs/paul/2014/05/public-types-explorer/ the 2) Metadata Explorer plug-in also lets you switch between searching for model types and public types then browse the attributes and associated objects - see http://platformadmin.com/blogs/paul/2012/08/metacoda-metadata-explorer-plug-in/ and http://www.metacoda.com/en/products/utility-plug-ins/metadata-explorer/
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