According to Kimball:
Dimensional models combine normalized and denormalized table structures. The dimension tables of descriptive information are highly denormalized with detailed and hierarchical roll-up attributes in the same table. Meanwhile, the fact tables with performance metrics are typically normalized. While we advise against a fully normalized with snowflaked dimension attributes in separate tables (creating blizzard-like conditions for the business user), a single denormalized big wide table containing both metrics and descriptions in the same table is also ill-advised.
This is also OK, by fazalhp at GeekInterview:
The main funda of DW is de-normalizing the data for faster access by the reporting tool...so if ur building a DW ..90% it has to be de-normalized and [of] course the fact table has to be de normalized...
To what extent and why are fact tables normalized or de-normalized?
From the point of relational database design theory, dimension tables are usually in 2NF and fact tables anywhere between 2NF and 6NF.
However, dimensional modelling is a methodology unto itself, tailored to:
one use case, namely reporting
mostly one basic type (pattern) of a query
one main user category -- business analyst, or similar
row-store RDBMS like Oracle, SQl Server, Postgres ...
one independently controlled load/update process (ETL); all other clients are read-only
There are other DW design methodologies out there, like
Inmon's -- data structure driven
Data Vault -- data structure driven
Anchor modelling -- schema evolution driven
The main thing is not to mix-up database design theory with specific design methodology. You may look at a certain methodology through database design theory perspective, but have to study each methodology separately.