The Compound of Three 16-Cells
Introduction.
This pretty model shows the self-duality of the 24-cell in grand fashion. One one hand, centers of the 24 octahedra in a 24-cell coincide with concurrent intersections of three mutually perpendicular axes whose endpoints are the vertices of these octahedra, while, on the other, the aforementioned endpoints themselves are the centers of the octahedra in the dual of the 24-cell. The 24-cell is isomorphic to its dual, but there is no natural isomorphism!
This model is closely related to the triality of 16-cells and the 24-cell with 3-fold symmetry. Having this models on hand helps to understand this model. One should also remember that this compound is the first stellation of the 24-cell, somewhat analogous to the compound of two tetrahedra being the first stellation of the regular octahedron.
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The pictured model uses 36 long blue struts, 36 long yellow struts, 36 long red struts, 36 medium red struts, 8 orange connectors, 8 green connectors, 8 purple connectors, and 24 white connectors. We use different-colored connectors to distinguish the 16-cells. Thus, one of the 16-cells has 8 green connectors as vertices, another has red connectors, etc.
This model has some false vertices. One might be able to see in the photos that some of the struts are forced to bend around each other. If you have some extremely small red struts and a few more connectors, then you might choose to represent these intersections by connectors.