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English: The function z = -x^6-3*x^4*y^2-3*x^2*y^4-6*x^2*y-y^6+2*y^3 has an inflection point at the origin where there are three directions to go uphill and three directions to go downhill. Such a point is named a 'monkey saddle' since a monkey would need two places to put its legs and one for its tail.
I found the formula by multiplying three paraboloids together.