This describes a construction that coincides with a 120-cell framework. This construction is explained more fully Here
Scenes shows the progression from a Rhombic Triacontahedron, first with a prismatic “stick” placed on one face, then a total of 30 sticks surrounding the RT. From there, frames of affine dodecahedra are added, first on 3-fold axes, then on 5-fold axes. The last scene shows a convex hull of the resulting 120-cell framework.

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30 piece construction coinciding with 120-cell framework