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I would like to make a picture of a truncated octahedron using ConvexHullMesh as follows:

ConvexHullMesh[{{3, 1, 1}, {1, 3, 1}, {1, 1, 3}, {-3, -1, 1}, {-1,-3, 1}, {-1, -1, 3}, {-3, 1, -1}, {-1, 3, -1}, {-1, 1, -3}, {3, -1,-1}, {1, -3, -1}, {1, -1, -3}}]

This gives a picture in which the hexagonal faces are subdivided into triangles. How to I make an image with no extra lines on the hexagons?

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You can use the undocumented option FlatFaces -> False:

ConvexHullMesh[{{3, 1, 1}, {1, 3, 1}, {1, 1, 3}, {-3, -1, 1}, {-1,-3, 1},
     {-1, -1, 3}, {-3, 1, -1}, {-1, 3, -1}, {-1, 1, -3}, {3, -1,-1},
     {1, -3, -1}, {1, -1, -3}}, 
   FlatFaces -> False] 

enter image description here

I learned about this option for the function ConvexHull3D from this answer by J.M.. It also works with ConvexHullMesh.

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