L. Lambán, V. Pascual, J. RubíoAuthors Info & Claims
Given d + 1 sets of points, or colours, S 1 , , S d + 1 in R d , a colourful simplex is a set T i = 1 d + 1 S i such that | T S i | 1 for all i { 1 , , d + 1 } . The colourful Carathéodory theorem states that, if 0 is in the convex hull of each S i , ...
We show that for every simplicial polytope an inscribed simplicial polytope exists that has the same dimension, number of vertices, number of edges, and number of 2-faces. This proves that the g-theorem for simplicial polytopes also holds for the class ...
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