What does "radical cube zero" mean?

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My hobby is taking comics way too seriously. And I just came across a math topic. In a certain comic (Fantastic Four 51, according to some polls the greatest comic issue ever) there's a machine for entering other dimensions. Its inventor describes it as "a radical cube". So I Googled "radical cube" and I keep finding technical references to "radical cube zero" and "diminishing radical cube" in the context of mathematical dimensions. E.g. here: http://cds.cern.ch/record/1059354 I understand that "radical" in maths refers to roots, but what is "diminishing radical cube" or "radical cube zero"?

Thanks for any explanation. I asked the question on Reddit, and all they could do was point me here. :)