Creating and handling new types of grid configurations might be an important topic, as Grasshopper is not supporting them natively (yet). I tried to create some semi-regular tessellations based on regular grids. It is actually truncated versions of regular grids, but it slowly becomes interesting as I realized that I may further truncate emerging grids to create Level 2 and Level 3 grids with more complex tessellations. Here are two examples of Level 1, truncating regular tessellations of squares and hexagons. Then, I tested Level 2, further truncating those semi-regulars. This seems to be a fast and efficient way of creating complex grids if you are not planning to get into procedural algorithms or scripting. Here are my Grasshopper files for Level 1 truncation [GHX: 0.8.0066] and Level 2 [GHX: 0.8.0066]