Above the spherical 120-cell is shown in stereographic projection where the centre of projection is the centre of the outer dark blue cell. Compare this with http://www.geom.uiuc.edu/graphics/pix/General_Interest/Digital_Art/sullivan-120cell.html.The spherical 120-cell has 120 dodecahedral cells. Apart from the outer cell in dark blue, that fills the outer space, they are hardly recognizable, so we shall split it up in many separate pictures of subsets of dodecahedral cells. We start with the 30 cells the fourth coordinate of which centres equals 0. Their 30 centres are the 30 vertices of an icosidodecahedron. The 30 dodecahedra around these vertices look like this: (the coloring is arbitrarily)

The 120-cell has 72 chains of 10 cells that are are connected by a pentagonal plane. One can choose 12 chains of 10 cells in 10 different ways so that the 12x10 cells completely make up the 120 cells of the 120-cell.

A chain of 10 dodecahedral cells in the spherical 120-cell whose cells are a subset of 30 cells above:

Another chain of 10 dodecahedral cells in the spherical 120-cell, containing the cell opposite to the cell from which centre we project the 120-cell:( the small dark blue one in the middle)

Another 2 chains of 10 dodecahedral cells in the spherical 120-cell are shown below. The left one has its centres in the x-z-plane and the right one has its centres in the  y-z-plane:

Another chain of 10 dodecahedral cells in the spherical 120-cell with their centres in the x-z-plane  :

Combining the last 2 chains results in two chains of 10 dodecahedral cells in the spherical 120-cell with their centres lying on 2 circles making a Hopf link (the circles lie in 2 mutually orthogonal planes):

Another set of 2 orthogonal chains of 10 dodecahedral cells in the spherical 120-cell:

In another direction:

Below are all the 30 dodecahedra with their centres in the x-z-plane:

Their 30 centres are the stereographic projection of the 30 vertices of an icosidodecahedron. There are 15 possible planes like this one. These planes are perpendicular to the 15 2-fold rotation axes of the icosahedral group on which lie 2 vertices of the undistorted icosidodecahedron. There are 20 more pairs of antipodal vertices on the hypersphere that lie on 3-fold rotation axes of the icosahedral group and 24 more pairs of antipodal vertices on the hypersphere that lie on 5-fold rotation axes of the icosahedral group. This corresponds to 59 projections of icosidodecahedra. Together with the undistorted icosidodecahedron itself this sums up to 60. The 120-cell admits 60 spheres with 30 centres of cells at the vertices of an icosidodecahedron.

In the icosidodecahedron there are also 10 great circles with 6 vertices on it and one can make a bead of 6 dodecahedra with these 6 vertices as their centres. The 6 cells are joined by 6 (yellow) edges of the 120-cell :

Another 2 examples: