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The answer is negative. Example:$$\max\{ 0,|y|,|x|-1\}.$$$$\max\{ |y|,|x|-1\}.$$
This is a convex piecewise linear function
which is not a convex combination of your "tripods", and not a limit of such combinations.
The answer is negative. Example
$$\max\{ 0,|y|,|x|-1\}.$$
The answer is negative. Example:$$\max\{ |y|,|x|-1\}.$$
This is a convex piecewise linear function
which is not a convex combination of your "tripods", and not a limit of such combinations.
