Optimal Way of Verifying a 3D Mesh Convex

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There are numerous questions on stack overflow similar to this problem already, but most are creating a convex hull, or checking in 2D Space.

I already have created an algorithm to create a 3D Convex Hull given the original Mesh's vertices, and checking if the final hull is identical to the original. However, its pretty inefficient, and I was wondering if there was some optimal way of verifying the convexity of the original.

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