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5

From V12, there is an inbuilt function RandomPolygon RandomPolygon[7] returns a simple polygon with seven sides. Other types are "Convex", "StarShaped". Table[Graphics[p, ImageSize -> 100], {p, RandomPolygon[{"Simple", 5}, 3]}], Table[Graphics[p, ImageSize -> 100], {p, RandomPolygon[{"Convex", 5}, 3]}], Table[...


4

NMaximize[] is not necessary to compute the positions of the major and minor axes of the ellipse. One only needs to perform an eigendecomposition: Nodes = {{0, 0}, {48, 44}, {48, 60}, {0, 44}}; ellipsoidBR = BoundingRegion[Nodes, "FastEllipsoid"]; center = ellipsoidBR[[1]]; {vals, vecs} = Eigensystem[ellipsoidBR[[2]]]; {a, b} = Sqrt[vals]; major = {...


5

Nodes = {{0, 0}, {48, 44}, {48, 60}, {0, 44}}; ellipsoidBR = BoundingRegion[Nodes, "FastEllipsoid"]; RegionMember[ellipsoidBR, {x, y}] (x | y) ∈ Reals && 499 x^2 + 576 (-44 + y) y <= 48 x (-56 + 15 y) Or Nodes = {{0, 0}, {48, 44}, {48, 60}, {0, 44}}; ellipsoidBR = BoundingRegion[Nodes, "FastEllipsoid"]; ellipsoidB = ...


7

As a workaround you can use the finite element mesh generator: Needs["NDSolve`FEM`"] coordinateList = Tuples[{Range[3], Range[3], Range[3]}]; MeshRegion[ToElementMesh[coordinateList], PlotTheme -> "Lines"]


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