I just came across something I hadn't seen before, on this Wikipedia page. There's a table comparing circular trig functions to hyperbolic trig functions (scroll to the bottom), and their utility for doing coordinate transformations, group properties etc., which is pretty familiar to people experienced in SR. But it also includes a column for parabolic trig functions, which it says can be used for Newtonian space-time. In this case, the isotropy type is shears, as opposed to rotations for circular trig transformations and boosts for hyperbolic transformations. This makes some intuitive sense, since I can imagine a 2-d Newtonian space-time diagram, where a moving frame would have an inclined t-axis, as usual, but its x-axis would still be parallel to the rest frame's x-axis, due to the absolute nature of simultaneity in Newtonian (or Galliean) space-time. I haven't thought any further about it, but I'm curious. Has anyone else run across this before?