Mathematics for the afterlife

Solution 1:

This is very useless. It is basically the (fibrated) boundary of the intersection of eight $2$-spheres. It can be generalized to higher dimensions but remains to be useless in all of those dimensions.

However, assuming we enter paradise, I would absolutely go to town on this thing. I would explore the properties of this shape in all of their useless beauty...

...I would investigate it as a symplectic object and study torsion on it. I would study it as a more rigid object using a non-contractible riemannian metric. I would do analysis on the force needed to crush this object and also study metric decay as the geometry becomes more and more random. I would study it as a network. I would study spaces where this object is a point in that space. I would also investigate every topological and algebraic property of the object. Lastly, I would explore the dynaimcs of an algebraic space in which this object is a point and the points "spin" via different moments, like an electron and I'd study and classify all the force mediating "particles" in said space. I would study a lot more about this object but time is money.