I don't know for sure, but I generally expect "hyper" in mathematics to mean "extended into an extra dimension".

A Hypercube is a 4-dimensional cube. A hypergraph is a graph with 3 (or more) vertices per edge, instead 2-vertices. Finally, a "Hypercardioid" is a cardioid, except in 3 dimensions (instead of the typical 2-dimensions).

https://en.wikipedia.org/wiki/Cardioid