I'm looking for a corresponding shape that follows a certain pattern of stepping up dimensions, but I'm stuck on the parts in 4d becuase I don't understand the pattern. The most important part is the first blank.

2 dots on a line are a slice of a circle in 2d

2 concentric circles on a plane are a slice of a torus in 3d

2 concentric spherical shells in 3d are a slice of _____________ in 4d?

3 dots on a line are a slice of a figure 8 in 2d

3 concentric circles on a plane would be a slice of a figure 8 torus looking like 2 concentric touching torus (tori?)

3 concentric sphere shells would be a slice of ___________ in 4d?

N dots :: N looped figure

N circles :: N rippled Torus

N sphere shells :: N _______________

If i could draw this might make more sense, but then again, I'm a lousy artist.