For more information on US GAAP Taxonomy Information Models, see this blog post. For more information on how the US GAAP Taxonomy information models map to the more general Business Reporting Logical Model, see here.
Number  Item  Item Description  Other 
1.  Hierarchy 
Used to model a hierarchy such as accounting policies, certain types of disclosures, etc. Contains no computations. Equivalent to the BRLM Hierarchy. See here for more information. 

2.  Roll Up 
Used to model a roll up. A Roll Up is a computation in the form: A + B + n = Total. For example, a balance sheet, income statement, and certain types of disclosures. Equivalent to the BRLM Roll Up. See here for more information. 

3.  Roll Forward 
Used to model a roll forward. Sometimes also called a movement analysis. A Roll Forward is a computation in the form: Beginning Balance + Changes = Ending Balance. For example, a cash flow statement, statement of changes in equity, and certain types of disclosures. Equivalent to the BRLM Roll Forward. 

4.  Compound Fact 
Not 100% certain that this is a meta pattern. (I think I am starting to see another "layer".) Models a compound fact, or facts which are used together and are "connected". For example, director's and their compensation or subsequent events. Equivalent to the BRLM Compound Fact. See here for more information. 

5.  Adjustment 
Used to model an adjustment. An Adjustment is a computation in the form: Origionally Stated Balance + Adjustment = Restated Balance. A prior period adjustment due to an accounting error or change in accounting policies is an example. Equivalent to the BRLM Adjustment. See here for more information. 

6.  Variance 
Used to model an variance. An Variance is a computation in the form: Actual  Budgeted = Variance. Equivalent to the BRLM Variance. See here for more information. 

7.  Other Relations 
Used to model other relations where computations exist. For example, the computation of weighted average shares or earnings per share are examples. Equivalent to the BRLM Variance. See here for more information. 