ROSECODE 446
Generalized ellipse 2
The definition of n-ellipse is as below: given n points (called foci) in a plane, an n-ellipse is the locus of all points of the plane whose sum of distances to the n foci is a constant. We can generalize the definition from plain to space, and the set of all points satisfying the constraint become a surface.
There is a tetrahedron ABCD of edge length 1 in a space. A 4-ellipse surface is the set of all points of the same space whose sum of distances to the 4 points A, B, C and D is 4 (see the blue solid in the picture).
Find the enclosed volume and surface area of the closed surface above. Give your answer rounded to 6 digits after the decimal point.
Answer format: [volume],[surface area]
Example: 4.188790,12.566371 for a sphere of radius 1.
There is a tetrahedron ABCD of edge length 1 in a space. A 4-ellipse surface is the set of all points of the same space whose sum of distances to the 4 points A, B, C and D is 4 (see the blue solid in the picture).
Find the enclosed volume and surface area of the closed surface above. Give your answer rounded to 6 digits after the decimal point.
Answer format: [volume],[surface area]
Example: 4.188790,12.566371 for a sphere of radius 1.