The following image is a part of Microsoft SQL Server 2008 R2 System Views. From the image we can see that the relationship between sys.partitions and sys
SELECT *
FROM sys.indexes i
JOIN sys.partitions p
ON i.index_id = p.index_id
JOIN sys.allocation_units a
ON a.container_id = (CASE
WHEN a.type IN (1, 3)
THEN p.hobt_id
WHEN a.type IN (2)
THEN p.partition_id
ELSE NULL
END)