This is a semi-regular tessellation of vertex arrangement 4.8.8. Its octagonal and square forms are all generated from data lists provided by the new version of subdivide component (The old one was processing points in a different fashion. I don’t know why they changed that). Anyway, a lexical operation is needed to convert this list into a more useful one for this exercise. You can download the source definition here [2011_12_25_srtessela]. However, you need to define a surface in order to start it. The component labeled with “pattern” is actually the data list selector, which takes appropriate indexes to convert and generate a new list that the polyline component could understand.

Update: Here is an updated version of this Grasshopper definition: [GHX: 0.9.0072]