I am walking in circles with the question why wolframalpha gives me as geometric description of $$(x-y)^2+(x-z)^2+(z-y)^2-14=0$$ as the infinite cylinder and of $$(x-y)^2+(x-z)^2+(x-u)^2+(z-y)^2+(u-y)^2+(z-u)^2-30=0$$ a glome, i.e., 3 sphere. The first is unbounded and the second is compact but their defining equations are just extensions to the dimension of the first plus one.
How is that possible? I do not manage to see it at all.