'Star' Tessellations - Type 4

(click on the image for a larger version)

The above edge network is a faceting is of the dodecahedral cells present in a type 1 network (home to the 6, 4, 3, 4 tessellation).  A copy of this network superimposed on the original 6, 4, 3, 4 tessellation is linked here.   Alternatively, this network can be regarded as a quasi-stellation of a 12, 12, 3 tessellation, replacing each dodecagon with a dodecagram sized such that the outside parallel edges of the dodecagram are one unit apart, as in the diagram below showing a square face highlighted.

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Three tessellations can be formed using this network:

12/5, 3, 12/5, 6/5
K:-, B:156, C: 3 6 | 6/5

12/5, 4, 12/7, 4/3
K:-, B:156, C: 2 6/5 (3/2 : 3) |

4, 3/2, 4, 6/5
K:-, B:156, C: 3/2 6 | 2 = r'{3 : 6}

In each case, clicking onto the vertex figures above will show the sample cell superimposed on the above network.

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