Kernel quits upon computing RegionIntersection

Question

Using 12.1.1.0 on MacOS BigSur I observe quitting Mathematica kernels when evaluating RegionIntersections on two regions that apparently only touch.

Example for Regions that cause the Kernel to quit without throwing error messages:

RegionIntersection[ 
 Polyhedron[{{-14.481838045552937`, -3.8913713702921195`, 
    13.743481930417099`}, {-13.387327710535084`, -4.686579676023987`, 
    14.579613424294676`}, {-13.592704266151834`, -3.145108820945274`, 
    14.801904645288225`}, {-12.786161768700419`, -4.476126018218702`, 
    13.92490718079964`}, {-12.982315767496441`, -3.0038758320024415`, 
    14.137216281827229`}, {-13.831522463803132`, -3.716627016121334`, 
    13.126322670747593`}}, {{1, 2, 3}, {5, 4, 6}, {4, 5, 3, 2}, {3, 5,
     6, 1}, {4, 2, 1, 6}}], 
 Cuboid[{-13.2`, -6.`, 14.375`}, {-10.8`, -3.5999999999999996`, 
   15.625`}]]

These are the regions:

When I only slightly change the coordinates to get regions that either overlap or do not overlap at all, I get the intersection polyhedron or the empty region indicator instead.

These are the regions that do overlap

RegionIntersection[ 
 Polyhedron[{{-14.481838045552937`, -3.8913713702921195`, 
    13.743481930417099`}, {-13.387327710535084`, -4.686579676023987`, 
    14.579613424294676`}, {-13.592704266151834`, -3.145108820945274`, 
    14.801904645288225`}, {-12.786161768700419`, -4.476126018218702`, 
    13.92490718079964`}, {-12.982315767496441`, -3.0038758320024415`, 
    14.137216281827229`}, {-13.831522463803132`, -3.716627016121334`, 
    13.126322670747593`}}, {{1, 2, 3}, {5, 4, 6}, {4, 5, 3, 2}, {3, 5,
     6, 1}, {4, 2, 1, 6}}], 
 Cuboid[{-13.25`, -6.`, 14.375`}, {-10.75`, -3.5999999999999996`, 
   15.625`}]]

with the corresponding output:

and the corresponding 3D graphics:

These are the regions that do not overlap

RegionIntersection[ 
 Polyhedron[{{-14.481838045552937`, -3.8913713702921195`, 
    13.743481930417099`}, {-13.387327710535084`, -4.686579676023987`, 
    14.579613424294676`}, {-13.592704266151834`, -3.145108820945274`, 
    14.801904645288225`}, {-12.786161768700419`, -4.476126018218702`, 
    13.92490718079964`}, {-12.982315767496441`, -3.0038758320024415`, 
    14.137216281827229`}, {-13.831522463803132`, -3.716627016121334`, 
    13.126322670747593`}}, {{1, 2, 3}, {5, 4, 6}, {4, 5, 3, 2}, {3, 5,
     6, 1}, {4, 2, 1, 6}}], 
 Cuboid[{-13.15`, -6.`, 14.375`}, {-10.85`, -3.5999999999999996`, 
   15.625`}]]

The output here is EmptyRegion, and the corresponding 3D graphics is:

Answer 1

Here are examples with v12.1.1 using exact values rather than machine precision

$Version

(* "12.1.1 for Mac OS X x86 (64-bit) (June 19, 2020)" *)

Clear["Global`*"]

rgn1 = Polyhedron[{{-14.481838045552937`, -3.8913713702921195`, 
      13.743481930417099`}, {-13.387327710535084`, -4.686579676023987`, 
      14.579613424294676`}, {-13.592704266151834`, -3.145108820945274`, 
      14.801904645288225`}, {-12.786161768700419`, -4.476126018218702`, 
      13.92490718079964`}, {-12.982315767496441`, -3.0038758320024415`, 
      14.137216281827229`}, {-13.831522463803132`, -3.716627016121334`, 
      13.126322670747593`}} // 
    Rationalize[#, 0] &, {{1, 2, 3}, {5, 4, 6}, {4, 5, 3, 2}, {3, 5, 6, 
     1}, {4, 2, 1, 6}}];

rgn2 = Cuboid @@ 
   Rationalize[{{-13.2`, -6.`, 14.375`}, {-10.8`, -3.5999999999999996`, 
      15.625`}}, 0];

rgn3 = RegionIntersection[rgn1, rgn2];

Volume[rgn3]

(* 3.91504*10^-8 *)

rgn4 = Cuboid @@ 
   Rationalize[{{-13.25`, -6.`, 14.375`}, {-10.75`, -3.5999999999999996`, 
      15.625`}}, 0];

rgn5 = RegionIntersection[rgn1, rgn4];

Volume[rgn5]

(* 0.00139939 *)

Answer 2

I observe a very similar behaviour with the following two regions:

When I try to run RegionIntersection on these regions, the computation takes more than 30 minutes. (I quit the kernel after this time, since for all other region pairs that I need to compute, the computations takes much less than a second). This is the corresponding command:

RegionIntersection[ 
 Cuboid[Rationalize[{-15.599999999999998`, 3.5999999999999996`, 
    13.125`}, 0], Rationalize[{-13.2`, 6.`, 14.375`}, 0]], 
 Polyhedron[
  Rationalize[{{-12.506721429921425`, 3.9624773092852443`, 
     15.656022698345078`}, {-13.443519981142686`, 4.706251231025362`, 
     14.640810221789032`}, {-13.649758588935882`, 3.158310171489477`, 
     14.864034492956131`}, {-12.837481483332462`, 4.494091809209582`, 
     13.980797468731524`}, {-13.034422783855483`, 3.0159324642645027`,
      14.193958713089975`}, {-11.942914132535591`, 3.783847471304209`,
      14.950243818178507`}}, 
   0], {{1, 2, 3}, {5, 4, 6}, {4, 5, 3, 2}, {3, 5, 6, 1}, {4, 2, 1, 
    6}}]]

Now, when I change the order of the Polyhedron and the Cuboid, I get an output, i.e. the kernel does not hang or stuck in the computation, but I don't get the desired result. Instead, I get:

The command that produces this output is:

RegionIntersection[
 Polyhedron[
  Rationalize[{{-12.506721429921425`, 3.9624773092852443`, 
     15.656022698345078`}, {-13.443519981142686`, 4.706251231025362`, 
     14.640810221789032`}, {-13.649758588935882`, 3.158310171489477`, 
     14.864034492956131`}, {-12.837481483332462`, 4.494091809209582`, 
     13.980797468731524`}, {-13.034422783855483`, 3.0159324642645027`,
      14.193958713089975`}, {-11.942914132535591`, 3.783847471304209`,
      14.950243818178507`}}, 
   0], {{1, 2, 3}, {5, 4, 6}, {4, 5, 3, 2}, {3, 5, 6, 1}, {4, 2, 1, 
    6}}], Cuboid[
  Rationalize[{-15.599999999999998`, 3.5999999999999996`, 13.125`}, 
   0], Rationalize[{-13.2`, 6.`, 14.375`}, 0]]]