The Title

The title, officially Invisible Handshake II, refers to the fact that the shape is topologically equivalent to the space between two hands that come together to grasp each other in a traditional handshake, but stop just short of touching. There are four large passages, in two pairs; they correspond to where the thumb and fingers of each hand would go. In the image below, one hand would go into the orange upper bowl and come out below the central skirt, while the other does the symmetrical thing from the lower blue bowl, emerging above the skirt.

The following images of a model show the two Y-shapes.