Also featured prominently in the marvel movies:
http://marvel-movies.wikia.com/wiki/Tesseract
And the movie "Cube 2: Hypercube"
http://www.imdb.com/title/tt0285492/
But in a non-fiction world, this is a hypercube:
http://en.wikipedia.org/wiki/Hypercube
It's just a multi-dimensional version of a cube. Not sure that there is a consciousness connection here, but the concept of how a 4-dimensional (and above) cube may appear is cool. We just can't visualize the 4th dimension of space so to us it's like drawing a cube on a flat piece of paper - without the context of the 3rd dimension, a drawing of a cube is just 2 squares connected by lines. A drawing of a hypercube looks like 2 cubes connected by lines, and we can't see it "properly" as it would really appear in 4-dimensional space.
I suppose a 4th density entity would see it correctly, and that's the only connection to "consciousness" I can think of.
Liv, just out of curiosity, why do you preface your posts with "Liv:"?