I have numerical data for 3D surfaces that I wish to mutually crop; i.e. crop the front and back with the left, right, top, and bottom - and similarly for the other 2 permutations. Afterwards, I will join these to make the surface of a volume. And later, I'll want to take unions and intersections of these volume surfaces.

What Built-in or supported-package symbols and functions can I use instead of writing my own package?

Here is some example low-resolution data:

(* Coordinate #1 is vertical, #2 is left to right, #3 is front to \
rear. *)
surfacenames = {"front", "back", "left", "right", "bottom", "top"};
lowressurfaces = {{{0., -0.7929, -1.1203}, {0., 0.0713, -1.1203}, {0.,
      0.9355, -1.1203}, {0.5, -0.7929, -0.7892}, {0.5, 
     0.0713, -0.7836}, {0.5, 
     0.9355, -1.1203}, {1., -0.7929, -0.4353}, {1., 
     0.0713, -1.1203}, {1., 0.9355, 0.027200}}, {{0., -0.7929, 
     0.8793}, {0., 0.0713, 0.8793}, {0., 0.9355, 
     0.8793}, {0.5, -0.7929, 0.5014}, {0.5, 0.0713, 0.8627}, {0.5, 
     0.9355, 0.7277}, {1., -0.7929, 0.9339}, {1., 0.0713, 
     0.9339}, {1., 0.9355, 
     0.9339}}, {{0., -0.7915, -1.1203}, {0., -0.7915, -0.0932}, {0., \
-0.7915, 0.9339}, {0.5, -0.7929, -1.1203}, {0.5, -0.7929, -0.0932}, \
{0.5, -0.7929, 
     0.9339}, {1., -0.5625, -1.1203}, {1., -0.7707, -0.0932}, {1., \
-0.7929, 0.9339}}, {{0., 0.9355, -1.1203}, {0., 0.9355, -0.0932}, {0.,
      0.9355, 0.9339}, {0.5, 0.9355, -1.1203}, {0.5, 
     0.9355, -0.0932}, {0.5, 0.9277, 0.9339}, {1., 
     0.9355, -1.1203}, {1., 0.9355, -0.0932}, {1., 0.9355, 
     0.9339}}, {{0., -0.7929, -1.1203}, {0., -0.7929, -0.0932}, {0., \
-0.7929, 0.9339}, {0., 0.0713, -1.1203}, {0., 0.0713, -0.0932}, {0., 
     0.0713, 0.9339}, {0., 0.9355, -1.1203}, {0., 
     0.9355, -0.0932}, {0., 0.9355, 
     0.9339}}, {{0.8992, -0.7929, -1.1203}, {0.9730, -0.7929, \
-0.0932}, {1., -0.7929, 0.9339}, {0.9860, 0.0713, -1.1203}, {1., 
     0.0713, -0.0932}, {1., 0.0713, 0.9339}, {1., 
     0.9355, -1.1203}, {1., 0.9355, -0.0932}, {1., 0.9355, 0.9339}}};