Consider the following polynomials: $$ f_1(n_1, m_1) = 30n_1m_1 + 23n_1 + 7m_1 + 5\\ f_2(n_2, m_2) = 30n_2m_2 + 17n_2 + 13m_2 + 7\\ f_3(n_3, m_3) = 30n_3m_3 + 23n_3 + 11m_3 + 8\\ f_4(n_4, m_4) = ...
Consider a n-simplex. For each edge (i,j), consider a n-ball, such that vertices i and j are antipodal on this ball. Is the simplex covered by the union of these balls? Thank you.