olap

As I am new to SSAS, have been reading an article on Multi-Dimension OLAP Cube and struggling to understand Cube concepts, It has been said that Although the term "cube" suggests three dimensions, a cube can have up to 64 dimensions. Could you please explain how is this possible on cube (other than 3-Dim example x,y,z planes)? Please don't give only links to study but also expecting some explanation. Don't think of a cube as a three-dimensional structure (despite the name). A "dimension" in a data warehouse situation is simply a varying value that you can use to access data in your warehouse.

I always thought that databases should be denormalized for read performance, as it is done for OLAP database design, and not exaggerated much further 3NF for OLTP design. PerformanceDBA in various posts, for ex., in Performance of different aproaches to time-based data defends the paradigm that database should be always well-designed by normalization to 5NF and 6NF (Normal Form). Have I understood it correctly (and what had I understood correctly)? What's wrong with the traditional denormalization approach/paradigm design of OLAP databases (below 3NF) and the advice that 3NF is enough for most