The Truncated 5-cell

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The truncated 5-cell is a cell-transitive polychoron formed by truncating a pentatope at one third of its edge length, so that its triangular faces become hexagons. New triangular faces form in place of the original vertices, forming new tetrahedral cells, and the original tetrahedral cells become truncated tetrahedra.

Structure

The following image shows the parallel projection of the truncated 5-cell into 3D:

The five tetrahedral cells are rendered in yellow, and are clearly visible here. Four of them appear to be flattened, due to foreshortening. They are regular tetrahedra in 4D.

The following images show where the truncated tetrahedral cells are:

Four of these cells also appear flattened due to foreshortening, but they are uniform truncated tetrahedra in 4D.

Perspective Projection

The following animation shows the perspective projection of the truncated 5-cell rotating in the ZW plane.

The red tetrahedron and one of the yellow tetrahedra appear to be turning inside-out and engulfing each other, but this is merely an artifact of the perspective projection. In 4D, they neither deform nor touch each other.