Let ∆(d, n) be the maximum possible edge diameter over all d-dimensional polytopes defined by n inequalities. The Hirsch conjecture, formulated in 1957, suggests that ∆(d, n) is no greater than n − d. No polynomial bound is currently known for ∆(d, n), the best one being quasipolynomial due to Kalai and Kleitman in 1992. Goodey showed in 1972 that ∆(4, 10) = 5 and ∆(5, 11) = 6, and more recently, Bremner and Schewe showed ∆(4, 11) = ∆(6, 12) = 6. In this follow-up, we show that ∆(4, 12) = 7 and present strong evidence that ∆(5, 12) = ∆(6, 13) = 7.
A new liquid crystal-based tileable display for large size full colour display applications such as electronic posters has been developed. High efficiency and long life are achieved through the use of light emitting diode backlighting and a novel woven optical fiber image converter that eliminates the need for colour filters.
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