I mean
r = TransformedRegion[Cuboid[], Function[p, {p[[1]]*(-p[[1]] + p[[2]] + p[[3]]), p[[2]]*(p[[1]] - p[[2]] + p[[3]]), p[[3]]*(p[[1]] + p[[2]] - p[[3]])}]]; Region[r] Unfortunately, this short code does not work for me in 13.2 on Windows 10.
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2 
- $\begingroup$ Mathematica quits itself during the execution. $\endgroup$user64494– user644942023-02-13 21:03:41 +00:00Commented Feb 13, 2023 at 21:03
- $\begingroup$ For me it gets OOM. It does not just "exit". Someone needs to try it with 64 GB of RAM. $\endgroup$Валерий Заподовников– Валерий Заподовников2023-02-14 09:58:32 +00:00Commented Feb 14, 2023 at 9:58
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2 Answers
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0 A workaround
$Version (* "13.2.1 for Mac OS X ARM (64-bit) (January 27, 2023)" *) Clear["Global`*"] r = ImplicitRegion[0 <= x <= 1 && 0 <= y <= 1 && 0 <= z <= 1, {x, y, z}]; r2 = TransformedRegion[r, Function[p, {p[[1]]*(-p[[1]] + p[[2]] + p[[3]]), p[[2]]*(p[[1]] - p[[2]] + p[[3]]), p[[3]]*(p[[1]] + p[[2]] - p[[3]])}]] (* ParametricRegion[{{x (-x + y + z), y (x - y + z), (x + y - z) z}, 0 <= x <= 1 && 0 <= y <= 1 && 0 <= z <= 1}, {x, y, z}] *) Region[r2] 
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Edit
- To get a more smooth surface, we use
RegionPlot3Dand useDisplayFunctionto transform the region.
RegionPlot3D[ BoundaryDiscretizeRegion[Cuboid[], MaxCellMeasure -> .01], DisplayFunction -> ReplaceAll[{x_Real, y_Real, z_Real} :> {x (-x + y + z), y (x - y + z), z (x + y - z)}], Boxed -> False, MaxRecursion -> 2] 
- Transform the
Dodecahedron.
reg = PolyhedronData["Dodecahedron", "Region"]; RegionPlot3D[ BoundaryDiscretizeRegion[reg, MaxCellMeasure -> .01], DisplayFunction -> ReplaceAll[{x_Real, y_Real, z_Real} :> {x (-x + y + z), y (x - y + z), z (x + y - z)}], MaxRecursion -> 2, Boxed -> False] 
Original
- We can
DiscretizeRegiontheCuboid[]at first.
Clear[r]; r = TransformedRegion[DiscretizeRegion@Cuboid[], Function[ p, {p[[1]]*(-p[[1]] + p[[2]] + p[[3]]), p[[2]]*(p[[1]] - p[[2]] + p[[3]]), p[[3]]*(p[[1]] + p[[2]] - p[[3]])}]]; Region[r] 
- Test another reg,for example some polyhedrons.
Clear[reg, r]; reg = PolyhedronData["Dodecahedron", "Region"]; r = TransformedRegion[DiscretizeRegion[reg], Function[ p, {p[[1]]*(-p[[1]] + p[[2]] + p[[3]]), p[[2]]*(p[[1]] - p[[2]] + p[[3]]), p[[3]]*(p[[1]] + p[[2]] - p[[3]])}]]; {reg, Region[r]} 
