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in this review, we discuss the use of a variety of 3-d models (particularly 3-d skin, lung, breast and endothelial) in radiobiological research and highlight the differences in responses compared to 2-d culturing conditions (monolayers). we review the characteristics of existing 3-d models and aim to point out the substantial advantages 3-d cultures provide for modern radiobiology. in particula...

We completely solve the problem of enumerating combinatorially inequivalent d-dimensional polytopes with d + 3 vertices. A first solution of this problem, by Lloyd, was published in 1970. But the obtained counting formula was not correct, as pointed out in the new edition of Grünbaum’s book. We both correct the mistake of Lloyd and propose a more detailed and self-contained solution, relying on...