The interior of this object is the traditional setting of the Banach-Tarski paradox. This object has constant positive Gaussian curvature, and it has the greatest possible volume to surface area ratio. Triangles in this type of geometry have angles summing to greater than three hundred sixty degrees. For 10 points, name this three-dimensional shape, the volume of which is four-thirds pi times the cube of the radius.
The interior of this object is the traditional setting of the Banach-Tarski paradox. This object has constant positive Gaussian curvature, and it has the greatest possible volume to surface area ratio. Triangles in this type of geometry have angles summing to greater than three hundred sixty degrees. For 10 points, name this three-dimensional shape, the volume of which is four-thirds pi times the cube of the radius.
The interior of this object is the traditional setting of the Banach-Tarski paradox.
{sphere} [or {spherical}]