The Bitruncated 5-cell

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The bitruncated 5-cell is a cell-transitive polychoron formed by truncating a pentatope at halfway to the depth that would yield a dual pentatope. It is bounded by 10 truncated tetrahedra in two groups of 5, with the groups corresponding to the cells of a pentatope and its dual, respectively.

Projections

The following image shows the cell-first perspective projection of the bitruncated 5-cell into 3D:

For clarity, we have omitted cells that lie on the far side of the polytope. The nearest cell to the 4D viewpoint is a truncated tetrahedron, shown below:

Surrounding this cell are 4 other truncated tetrahedrea, as shown below:

These cells look flattened because of foreshortening by the perspective projection. They are actually all uniform truncated tetrahedra. They are joined to each other by triangular faces.

The triangular faces of these 4 cells are connected to the antipodal truncated tetrahedron lying on the opposite side of the polychoron:

As can be seen, the antipodal truncated tetrahedron lies in a dual orientation to the nearest truncated tetrahedron.

The triangular faces of the nearest cell, on the other hand, are connected to the four cells surrounding the far-side cell, shown below:

For reference, we have included the farthest cells in these images.

Comparing these images with the earlier ones, we see that these cells are joined to the four cells surrounding the nearest cell by their hexagonal faces.

Altogether, these are the 10 cells that bound the bitruncated 5-cell.

Properties

The bitruncated 5-cell is one of the cell-transitive uniform polychora that aren't regular. Besides the n,n-duoprisms, the other such polychoron is the bitruncated 24-cell.