Runcinated tesseracts

The runcinated tesseract or (small) disprismatotesseractihexadecachoron has 16 tetrahedra, 32 cubes, and 32 triangular prisms.

The cube-first orthographic projection of the runcinated tesseract into 3-dimensional space has a (small) rhombicuboctahedral envelope.

In the process, the tetrahedra expand into cuboctahedra, and triangular prisms fill in the remaining gaps.

The runcitruncated 16-cell may be constructed by contracting the small rhombicuboctahedral cells of the cantellated tesseract radially, and filling in the spaces between them with cubes.

In the process, the octahedral cells expand into truncated tetrahedra (half of their triangular faces are expanded into hexagons by pulling apart the edges), and the triangular prisms expand into hexagonal prisms (each with its three original square faces joined, as before, to small rhombicuboctahedra, and its three new square faces joined to cubes).

The vertices of a runcitruncated 16-cell having an edge length of 2 is given by all permutations of the following Cartesian coordinates: The small rhombicuboctahedral cells are joined via their 6 axial square faces to the cubical cells, and joined via their 12 non-axial square faces to the hexagonal prisms.

Finally the 4 types of cells exist centered on the 4 corners of the fundamental simplex.

[2] The bialternatosnub 16-cell or runcic snub rectified 16-cell, constructed by removing alternating long rectangles from the octagons, is also not uniform.

[3] A variant with regular icosahedra and uniform triangular prisms has two edge lengths in the ratio of 1 : 2, and occurs as a vertex-faceting of the scaliform runcic snub 24-cell.