TITLE: What do globes (used to construct globular sets, $\omega$-categories, etc.) actually look like?
QUESTION [7 upvotes]: Nlab introduces the globular category as a geometrical model to construct certain higher categorical structures (e. g. strict $\omega$-categories), just as quasi-categories, for example, are modelled on simplices. However, I didn't find much information on the geometric intuition behind their definition.
So, what do these globes really look like? More precisely, how is the geometric realization of globular sets obtained?

REPLY [5 votes]: The paper on the fundamental globular groupoid of a filtered space has some pictures, and a definition of the simplicial nerve of a globular $\omega$-groupoid. Relations with other areas are in the paper M. Kapranov, "Membranes and higher groupoids" arxiv 1602.06166 .  My own philosophy is spelled out in this Aveiro presentation. 
See also this discussion.