Mathematical Experiment 11

Construct a regular tetrahedron together with sphere tangent to its edges.

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Construct the part of the sphere in the above problem inside the tetrahedron

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Construct a cube together with sphere tangent to its edges.

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Construct the part of the sphere in the above problem inside the cube.

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Arrange six identical "caps" of a sphere as thus:

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Four mutually tangent spheres of the same size, cutoff by planes determined by each triplets of points of tangency.

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