2 added 48 characters in body
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The (undocumented!) function ComputationalGeometry`Methods`ConvexHull3D[] is up to the task for this particular case:

ComputationalGeometry`Methods`ConvexHull3D[pts, Axes -> None,
                                           Graphics`Mesh`FlatFaces -> False]

some convex polyhedron

The (undocumented!) function ComputationalGeometry`Methods`ConvexHull3D[] is up to the task for this particular case:

ComputationalGeometry`Methods`ConvexHull3D[pts, Axes -> None, Graphics`Mesh`FlatFaces -> False]

some convex polyhedron

The (undocumented!) function ComputationalGeometry`Methods`ConvexHull3D[] is up to the task for this particular case:

ComputationalGeometry`Methods`ConvexHull3D[pts, Axes -> None,
                                           Graphics`Mesh`FlatFaces -> False]

some convex polyhedron

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The (undocumented!) function ComputationalGeometry`Methods`ConvexHull3D[] is up to the task for this particular case:

ComputationalGeometry`Methods`ConvexHull3D[pts, Axes -> None, Graphics`Mesh`FlatFaces -> False]

some convex polyhedron