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The cells of the 4D polytope consist of these three types of cells.
The cells are all Archimedean solids.
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Here are all the cells constructed, ready to be glued together.
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Start with a truncated cuboctahedron (blue), and glue other cells to
every face. I recommend attaching the smallest cells first (the red
triangular prisms). Be careful to get the orientation right.
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Then attach the medium sized cells (the yellow truncated tetrahedra).
Again being careful with the orientation.
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Then attach 6 more truncated cuboctahedra to the first. Being careful
once more with the orientation. At this point the original truncated
cuboctahedron is completely hidden. Proceed to attach the remaining
cells, taking care to place them correctly.
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Here's what the 4D polytope looks like projected into 3D, and with the
blue truncated cuboctahedra hidden.
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