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added 6 characters in body

edited Apr 28, 2024 at 10:07

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Edit

To get a more smooth surface, we use RegionPlot3D and use DisplayFunction to transform the region.

RegionPlot3D[BoundaryDiscretizeRegion@Cuboid[]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)}], PlotPointsBoxed -> 60False, MaxRecursion -> 2, Boxed -> False]2]

Transform the Dodecahedron.

reg = PolyhedronData["Dodecahedron", "Region"]; RegionPlot3D[ BoundaryDiscretizeRegion@regBoundaryDiscretizeRegion[reg, MaxCellMeasure -> .01],  DisplayFunction -> ReplaceAll[{x_Real, y_Real, z_Real} :> {x (-x + y + z), y (x - y + z), z (x + y - z)}], PlotPointsMaxRecursion -> 802,  MaxRecursion -> 6, Boxed -> False]

Original

We can DiscretizeRegion the Cuboid[] 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]}

Edit

To get a more smooth surface, we use RegionPlot3D and use DisplayFunction to transform the region.

RegionPlot3D[BoundaryDiscretizeRegion@Cuboid[], DisplayFunction -> ReplaceAll[{x_Real, y_Real, z_Real} :> {x  (-x + y + z), y  (x - y + z), z  (x + y - z)}], PlotPoints -> 60, MaxRecursion -> 2, Boxed -> False]

Transform the Dodecahedron.

reg = PolyhedronData["Dodecahedron", "Region"]; RegionPlot3D[ BoundaryDiscretizeRegion@reg, DisplayFunction -> ReplaceAll[{x_Real, y_Real, z_Real} :> {x (-x + y + z), y (x - y + z), z (x + y - z)}], PlotPoints -> 80,  MaxRecursion -> 6, Boxed -> False]

Original

We can DiscretizeRegion the Cuboid[] 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]}

Edit

To get a more smooth surface, we use RegionPlot3D and use DisplayFunction to 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 DiscretizeRegion the Cuboid[] 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]}

added 11 characters in body

edited Feb 26, 2024 at 6:05

91.7k
6
113
194

Edit

To get a more smooth surface, we use RegionPlot3D and use DisplayFunction to transform the region.

RegionPlot3D[DiscretizeRegion@Cuboid[]RegionPlot3D[BoundaryDiscretizeRegion@Cuboid[], DisplayFunction -> ReplaceAll[{x_Real, y_Real, z_Real} :> {x  (-x + y + z), y  (x - y + z), z  (x + y - z)}], PlotPoints -> 60, MaxRecursion -> 42, Boxed -> False]

Transform the Dodecahedron.

reg = PolyhedronData["Dodecahedron", "Region"]; RegionPlot3D[ BoundaryDiscretizeRegion@reg, DisplayFunction -> ReplaceAll[{x_Real, y_Real, z_Real} :> {x (-x + y + z), y (x - y + z), z (x + y - z)}], PlotPoints -> 80, MaxRecursion -> 6, Boxed -> False]

Original

We can DiscretizeRegion the Cuboid[] 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]}

To get a more smooth surface, we use RegionPlot3D and use DisplayFunction to transform the region.

RegionPlot3D[DiscretizeRegion@Cuboid[], DisplayFunction -> ReplaceAll[{x_Real, y_Real, z_Real} :> {x (-x + y + z), y (x - y + z), z (x + y - z)}], PlotPoints -> 60, MaxRecursion -> 4, Boxed -> False]

Transform the Dodecahedron.

reg = PolyhedronData["Dodecahedron", "Region"]; RegionPlot3D[ BoundaryDiscretizeRegion@reg, DisplayFunction -> ReplaceAll[{x_Real, y_Real, z_Real} :> {x (-x + y + z), y (x - y + z), z (x + y - z)}], PlotPoints -> 80, MaxRecursion -> 6, Boxed -> False]

We can DiscretizeRegion the Cuboid[] 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]}

Edit

To get a more smooth surface, we use RegionPlot3D and use DisplayFunction to transform the region.

RegionPlot3D[BoundaryDiscretizeRegion@Cuboid[], DisplayFunction -> ReplaceAll[{x_Real, y_Real, z_Real} :> {x  (-x + y + z), y  (x - y + z), z  (x + y - z)}], PlotPoints -> 60, MaxRecursion -> 2, Boxed -> False]

Transform the Dodecahedron.

reg = PolyhedronData["Dodecahedron", "Region"]; RegionPlot3D[ BoundaryDiscretizeRegion@reg, DisplayFunction -> ReplaceAll[{x_Real, y_Real, z_Real} :> {x (-x + y + z), y (x - y + z), z (x + y - z)}], PlotPoints -> 80, MaxRecursion -> 6, Boxed -> False]

Original

We can DiscretizeRegion the Cuboid[] 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]}

added 423 characters in body

edited Feb 26, 2024 at 5:59

91.7k
6
113
194

To get a more smooth surface, we use RegionPlot3D and use DisplayFunction to transform the region.

RegionPlot3D[DiscretizeRegion@Cuboid[], DisplayFunction -> ReplaceAll[{x_Real, y_Real, z_Real} :> {x (-x + y + z), y (x - y + z), z (x + y - z)}], PlotPoints -> 60, MaxRecursion -> 4, Boxed -> False]

Transform the Dodecahedron.

reg = PolyhedronData["Dodecahedron", "Region"]; RegionPlot3D[ BoundaryDiscretizeRegion@reg, DisplayFunction -> ReplaceAll[{x_Real, y_Real, z_Real} :> {x (-x + y + z), y (x - y + z), z (x + y - z)}], PlotPoints -> 80, MaxRecursion -> 6, Boxed -> False]

We can DiscretizeRegion the Cuboid[] 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]}

We can DiscretizeRegion the Cuboid[] 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]}

To get a more smooth surface, we use RegionPlot3D and use DisplayFunction to transform the region.

RegionPlot3D[DiscretizeRegion@Cuboid[], DisplayFunction -> ReplaceAll[{x_Real, y_Real, z_Real} :> {x (-x + y + z), y (x - y + z), z (x + y - z)}], PlotPoints -> 60, MaxRecursion -> 4, Boxed -> False]

Transform the Dodecahedron.

reg = PolyhedronData["Dodecahedron", "Region"]; RegionPlot3D[ BoundaryDiscretizeRegion@reg, DisplayFunction -> ReplaceAll[{x_Real, y_Real, z_Real} :> {x (-x + y + z), y (x - y + z), z (x + y - z)}], PlotPoints -> 80, MaxRecursion -> 6, Boxed -> False]

We can DiscretizeRegion the Cuboid[] 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]}

added 1 character in body

edited Feb 14, 2023 at 0:55

91.7k
6
113
194

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added 341 characters in body

edited Feb 14, 2023 at 0:50

91.7k
6
113
194

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answered Feb 14, 2023 at 0:39

91.7k
6
113
194

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