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Distribution of the number of vertices of a regular simplex. (Russian) Zbl 0626.60019
The authors compute for $$n=3$$ and $$k=1,2,3$$ the probability that exactly k vertices of the n-dimensional simplex are over a random hyperplane, drawn through its centroid. The randomness is introduced by the assumption that the normal vector of the hyperplane is uniformly distributed on the surface of the unit n-dimensional sphere.
Reviewer: L.Mutafchiev
##### MSC:
 60D05 Geometric probability and stochastic geometry
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