The 120-cell is the 4 dimensional analogue of the dodecahedron. Just as the dodecahedron has 2-dimensional faces (12 pentagons), the 120-cell has 3-dimensional faces (120 dodecahedra).
This is a model of what you get when you take the 120-cell drawn on the unit sphere in 4-dimensional space, throw half of the sphere away then stereographically project the remainder into our 3-dimensional space.
To get the whole 120-cell back, take two copies of this, and glue them together along their boundaries. You can see lots of half dodecahedra on the boundary of the model which form whole dodecahedra together with their mirror image in the other half.