Suppose one has to create a data warehouse for projects, what would be the dimensions and facts needed for that purpose?

you can use Earned Value measures to see how projects went in the past, categorise them by their objectives, know their relations (in many occations, projects are initiated as a result to another, as a requirement to perform another, or to complement another), and most importantly, realised benefits

 

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The various dimensions are; A conformed dimension: a set of data attributes that have been physically referenced in multiple database tables using the same key value to refer to the same structure, attributes, domain values, definitions and concepts.
A junk dimension: a convenient grouping of typically low-cardinality flags and indicators.
By creating an abstract dimension, these flags and indicators are removed from the fact table while placing them into a useful dimensional framework.
A degenerate dimension: a key, such as a transaction number, invoice number, ticket number, or bill-of-lading number, that has no attributes and hence does not join to an actual dimension table.
Role-playing dimension Dimensions are often recycled for multiple applications within the same database.
For instance, a "Date" dimension can be used for "Date of Sale", as well as "Date of Delivery", or "Date of Hire".
This is often referred to as a "role-playing dimension".

IT depends on what facts need to be interrogated.
What facts are core to the data warehouse? The product? Customer? Once you have established the core facts, then you can build the dimensions and measures you need.
Time range? Frequency?

I would start at the operational level.
First find out the data requirements (reports, forecasts and analytics) used by the departments, divisions and the management for their daily operations and targets.
Relevant data may come from multiple sources, databases or can even be excel sheets that may be stored on a client.
Once this information is gathered, it is easier to determine the dimensions of the required data warehouse based on the volume and validations of the transaction data as well as the master data.

One cannot simply list dimensions and facts. These all depends on what you are measuring and against what. By looking into the existing reports one can identify the dimensions and facts.

well its difficult, the purpose is to finish the project @ right time and resources, also having flexibility to balance between time and budget is needed.
all of dimensions are limited (time, resources, capital).

In Data warehousing- Database design has a definite key role in making the storage efficient- The Dimension and facts needed fur datawarehouse Create sound cooperate database,Crate communication network,Managing smooth data flow,and Do proper check and security measures for misuse.

I suppose what does dimensions really mean here, in the context of the subject we are talking about it is End result.
We need to define the scope of the project, which is completely depends on business need.
 In general sense business needs are accurate, complete and easy reporting from any DW.
Main reason for business sponsoring this project will be to have easy access all sources of data in their organisation.
I as a business analysis will look at reporting requirement of the business and on that base I will define the dimensions and facts.
Until we don’t know the really business need we can’t define dimensions or facts, it will be all hypothetical only.

You can use fact to save earned value mesures, actual cost vs planned cost and % progress of milestones. Dimensions can be date, milestones, employess ... etc