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ConvexHullMesh inconsistency

Discussion in 'Mathematics' started by Joseph O'Rourke, Aug 1, 2020 at 8:03 PM.

  1. I am seeing an inconsistency in ConvexHullMesh that I don't understand. Here is

    Rhull = ConvexHullMesh[pts8]


    where the $8$ points (at bottom of post) determine a regular octagon-base pyramid:

    [​IMG] As expected. When I change the base to a regular decagon instead
    Rhull = ConvexHullMesh[pts10]


    I get this:

    [​IMG] The hull is just $3$ of the $10$ faces.
    If it matters, I generate the points with sines & cosines converted with //N. I tried leaving the points symbolic without observing a difference.


    pts8={{1., 0., 0.}, {0.707107, 0.707107, 0.}, {0., 1., 0.},
    {-0.707107, 0.707107, 0.}, {-1., 0., 0.}, {-0.707107, -0.707107, 0.},
    {0., -1., 0.}, {0.707107, -0.707107, 0.},{0, 0, 1}};

    pts10={{1., 0., 0.}, {0.809017, 0.587785, 0.}, {0.309017, 0.951057,
    0.}, {-0.309017, 0.951057, 0.}, {-0.809017, 0.587785, 0.}, {-1., 0.,
    0.}, {-0.809017, -0.587785, 0.}, {-0.309017, -0.951057,
    0.}, {0.309017, -0.951057, 0.}, {0.809017, -0.587785, 0.}, {0., 0.,
    1.}};

    Version 12.1.0.0.

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