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It's a degenerate polyhedron. Their faces intersect and cross one another.

Soo it’s not a “real” shape? In the sense that I couldn't mold some clay into this form like I could with eg a football?

It was made out of paper sheets printed by the “Great Stella” software available elsewhere on the same site:

Given that the article is about making one out of paper, I'd say it is "real".

Clay might be a difficult material to use to make it though.

I'd imagine it could probably be made via CNC or 3D printing or similar.