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A typical OLAP cube looks like this:

enter image description here

As I can see, this cube can work with 2 or 3 dimensions, but what if I have 4 dimensions to produce facts?

Should I use star schema instead when having more than 3 dims?

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Your example is a star schema, it's just a star with three points (dimensions).

It's OK to have star schemas with more dimensions. Some large OLAP schemas can have tens of dimensions.

The star schema holds the underlying data. The cube is a convenient set of pre-aggregated values that make our run-time faster. The "cube" name is a handy visual and linguistic analogy but not a fundamental part of it's definition. Specifically, it is not limited to 3D. As in maths were a hypercube can be reasoned about in many dimension so an OLAP cube can be defined over many star schema dimensions. It just gets harder to draw in marketing literature, is all.

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