Here are shown some dissections and arrays of polar zonohedra with 12 directions. While there are many ways dissection can be done, here are patterns with symmetry about the polar axis.
The version of 132-hedron shown here has square faces, colored yellow, green faces that are Arc cos 1/3 = 70.528…° rhombi, purple faces that are Arc cos 2/3 = 48.189…° rhombi. White faces are less familiar angles. In the Scenes dropdown menu are some ways that polyhedra can be inscribed within the major cell.
In the model below, the Scenes menu shows a complete dissection of the 132-hedron as frame, and with some minor cells paneled, to be more visible. These dissections involve hexahedral and dodecahedral cells always using struts parallel with some of the 12 coordinate directions. Dissections could be made in many ways that are all hexahedral cells, but that generally reduces symmetry.
Arrays of polar 132-hedron cells can be composed with spaces between major cells occupied with subcells that bridge between major cells, and are all made with edges that are unit lengths parallel with some of the 12 coordinate directions. Two types of such arrays can be viewed here.Type 1 and Type 2 In Type 1, the rings of major cells surrounding the axis are connected to adjacent cells by shared faces. In Type 2, theses connections are by shared vertices.
An extended Type 1 array is shown below.
This is a continuation of a series of posts including This