1.4. AFFINE MANIFOLDS WITH SINGULARITIES 25 Figure 17 Figure 18 Figure 19 Then choose P so that each edge of P is subdivided into four line segments of aﬃne length 1, as in Figure 17. Then Δ consists of 24 points, one in the interior of each of these line segments. We can repeat this in higher dimension, say taking Ξ2 := Conv{(−1, −1, −1, −1), (4, −1, −1, −1),..., (−1, −1, −1, 4)}. Suppose P is chosen so that each 2-face of Ξ is triangulated by P as in Figure 18. Then Δ restricted to such a two-face is depicted in Figure 19. So far, these examples are all integral tropical manifolds. To obtain examples which are not integral, one can deform one of the above examples continuously.

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