Roman surface / Steiner surface

thingiverse

Four instances of this component merged together form a unit whose exterior is called Roman or Steiner surface (consult figure below). To learn more, check out: https://en.wikipedia.org/wiki/Roman_surface (Klein's bottle mentioned under "remix" as it could be worth exploring too). Instructions The Steiner surface also known as Roman surface can be defined using various equations, visit: https://en.wikipedia.org/wiki/Roman_surface Maple 18 provides a new feature to export plot results as STL files - it was used to generate this unit (utilizing the command plot3d and the equations for x,y,z in polar coordinates). with(plottools) p2 := plot3d([cos(u)*sin(v)*(cos(v)^2), sin(u)*cos(v)*sin(v), cos(u)*cos(v)*sin(v)], u = Pi/2 .. Pi, v = 0..Pi/2, grid = [144, 144]) # output size limited to 1 MB in academic edition stlp := "............stl" exportplot(stlp, p2) Important tip: To create and print your own units, spherical angles should be chosen so no point is generated twice (for instance, if phi=0..Pi is enough, then it shouldn't be extended to phi=-Pi..Pi). Otherwise, 3D printer software will not generate a useable .gcode.