Roman surface / Steiner surface

thingiverse

Four copies of this part together make an object, whose surface is called Roman or Steiner surface (see figure). For more information see: http://en.wikipedia.org/wiki/Roman_surface (Klein's bottle is mentioned under "remix" as it might be of interest as well). Instructions The Roman surface also known as Steiner surface can be described by different equations, see:http://en.wikipedia.org/wiki/Roman_surface Maple 18 offers the new feature to export plots outputs as STL files - it was used for creating this object (using the command plot3d and the equations for x,y,z in polar coordinates). with(plottools) p2 := plot3d([cos(u)sin(u)cos(v)^2, sin(u)cos(v)sin(v), cos(u)cos(v)sin(v)], u = (1/2)Pi .. Pi, v = 0Pi .. .5*Pi, grid = [144, 144]) # output size limited to 1 MB, at least in academic version stlp := "............stl" exportplot(stlp, p2) Important hint: If you want to create and print your own objects, the spherical angles should be chosen such that no point is generated twice (e.g. if phi=0..Pi is enough, then it should not be extended to phi=-Pi..Pi). Otherwise no useable .gcode could be created by the 3d printer software.