Subgroup diagram of S4 made out of cycle graphs

thingiverse

This is a comprehensive subgroup diagram of the symmetric group of order 24 (S_4) made up of cycle graphs based on the following image from wikiversity:\r\nhttps://en.wikiversity.org/wiki/Symmetric_group_S4#/media/File:Symmetric_group_S4;_lattice_of_subgroups_Hasse_diagram;_11_different_cycle_graphs.svg\r\n\r\nNeed to refresh your memory on the subject? Here are some relevant wiki-pages:\r\nhttps://en.wikiversity.org/wiki/Symmetric_group_S4\r\nhttps://en.wikipedia.org/wiki/Lattice_of_subgroups\r\nhttps://en.wikipedia.org/wiki/Cycle_graph_(algebra)\r\n\r\nThe color of each vertex indicates the conjugation-class of the corresponding element:\r\nblack = identity element\r\ngreen = 2 cycles\r\nblue = 3 cycles\r\nred = 4 cycles\r\nyellow = product of two disjoint 2 cycles\r\nThe color of each line connecting two subgroups gives the index of the smaller one in the other:\r\norange = index 2\r\nblue = index 3\r\ngreen = index 4\r\n\r\nNote that the orientation of the graphs hanging is crucial!\r\n\r\nTo generate these models, I wrote some Python code using the numpy-stl library.\r\n(see Python files in thing files) \r\nThe input is a graph containing just the coordinates of each vertex and the edges.\r\nThe output is a whole bunch of spheres with holes in exactly the right spot and pointy sticks with the right length. \r\nThe code is likely imperfect and poorly commented, so no guarantees!\r\nThough if anyone is a chemistry fan, the code should be applicable to making models of large molecules as well.\r\n\r\nNotes on files:\r\n- S4_subgroups_graph_STLs.zip contains all of the models generated by S4SubgroupsGraph.py. Each model should be printed once in the color of the name of its parent folder.\r\n- MeshCutter.py is a Python file used by GraphModelGenerator.py\r\n MeshCutter uses Sphere1.stl and Sphere2.stl\r\n- GraphModelGenerator.py has functions to make graphs\r\n- S4SubgroupsGraph.py contains the code to generate the\r\n- the .curaprofile files are the print settings I used to slice the models\r\n\r\nRequirements:\r\n- Python 3.x with libraries numpy (pip install numpy) and numpy-stl (pip install numpy-stl)\r\n- A slicer.\r\n- Five different colors for the best effect.\r\n- Fishing wire\r\n- A little bit of colored rope in red, green, and orange\r\n- see-through tape\r\n- some way to hang things on your ceiling\r\n\r\nPrint settings:\r\n- Ender 3 Pro.\r\n- Slicer: Ultimaker Cura\r\nAll my settings can be found in the .curaprofile files in the thing files section