spherical geometry promlem - repost

Hello, I'm interested in your project. What parameters are to be used to expressed the surface area? If I remember correctly in the previous post of the project the rounded corners were parts of spherical caps. There is no mentioning of that in the current post. Thank you Serge

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What is the nature of this project? Is this a school assignment? Does it need to be solved in closed/symbolic form? Can it be solved merely numerically? I'm also wondering if more criteria can be assumed to make the problem simpler, e.g.: with respect to curve P, can that curve be assumed to go through the center of the circles (well, spherical cap's axis where it meets the sphere) that define the corner arcs?

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