Truncated Pentachoron (18-Tip)

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Truncated Pentachoron (18-Tip)

The truncated pentachoron is number 18 in the list of uniform polychora in Stella4D, with the abbreviated name "tip". It has 10 cells: 5 tetrahedra (green) and 5 truncated tetrahedra (red). This model represents a perspective projection of the 4D polytope into 3D space, with just two truncated tetrahedral cells hidden to reveal the internal structure. The projection is tetrahedron-first. The model typically opens in Stella4D using truncated tetrahedron-first projection, so start by selecting a tetrahedral cell and using "4D→Projection Direction→Cell First".

The two hidden cells open up what appears to be a crystal cave. If we hid all the truncated tetrahedra, then the remaining tetrahedra would be floating in space on their own, so we need to keep some unhidden.

See this tutorial for some comments on obtaining nets for building paper models of 4D polytopes.

Here are the nets from Stella4D, printed onto coloured paper, scored, cut out, and folded.

Put the inner part together first.

Attach the inner part into the outer tetrahedral shell. Then simply glue the outer tetrahedron together.

Another view of the finished model.

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