Arrays of zonohedral cells in an eight directional system are shown. Type I has major cells that are 56-faced polar zonohedra, 2 of them connecting along the polar axis at shared vertices, and 8 cells arranged in a ring, sharing faces with adjacent cells. Space between the central chain of cells and the surrounding ring is filled with dodecahedral and hexahedral cells, with all edges being unit lengths parallel with some of the 8 coordinate directions.

This is a continuation of the series shown in 7 Directional Space Filling

Type I 8 Direction Array

In the figure below, section planes with polar axis normal to them show tilings of colored triangles with each traingle being a section of a hexahedron. There are 5 types of triangle, corresponding to 5 types of hexahedron.

A dissection of a 56-hedron into hexahedra

This shows a second type of array, Type II, with a single cell in the center, and a ring of 8 cells surrounding, but connected at shared verrtices with adjacents. Spaces between are occupied with dodecahedral and hexahedral cells, all with unit length edges, as with the Type I array

Type II Array

This shows an extended array of Type II, with many of the connecting cells omitted, for viewing.

Extended Type II Array

Likewise, an extended array of Type I is shown in the figure below, with many connecting cells left out for viewing.

In both of these types, it appears that these arrays, or variations of them, can be carried out without inherent limit.

Extended Type I Array

The figure below illustrates the zonal character of a whole array.

Type I array, with 4 distinct zones colored blue

A continuation of this series can be seen Here