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An embedded surface in R is projected into R with the double point set which includes a finite number of triple points. We consider the minimal number of such triple points among all projections of embedded surfaces which are ambient isotopic to a given surface and show that for any non-negative integer N there exists a 2-component non-orientable surface in R whose minimal triple point number is equal to 2N .

Minimal triple point numbers of some non-orientable surface-links