It is paracompact because it has infinite vertex figures, with all vertices as ideal points at infinity.
A half symmetry construction, [3,4,4,1+], exists as {3,41,1}, with two alternating types (colors) of octahedral cells: ↔ .
There are fifteen uniform honeycombs in the [3,4,4] Coxeter group family, including this regular form.
It is a part of a sequence of honeycombs with a square tiling vertex figure: It a part of a sequence of regular polychora and honeycombs with octahedral cells: The rectified order-4 octahedral honeycomb, t1{3,4,4}, has cuboctahedron and square tiling facets, with a square prism vertex figure.
The cantellated order-4 octahedral honeycomb, t0,2{3,4,4}, has rhombicuboctahedron, cube, and square tiling facets, with a wedge vertex figure.