Sphere



The sphere is a the rotatope with three round dimensions, and no flat dimensions. Hence, it is the 3D hypersphere. It can also be considered as being the set of all points that are the same distance from another point (the centre) in space. The volume of a sphere is 4pi/3 * r^3

Equation
A sphere of diameter

$$l$$ can be constructed by drawing the curve that satisfies

$$2\sqrt { 2({ x }^{ 2 }+{ y }^{ 2 }+{ z }^{ 2 }) } ={ l }$$ .

Hypervolumes

 * vertex count =$$N/A$$
 * edge length =$$N/A$$
 * surface area =$$\pi { l }^{ 2 }$$
 * surcell volume =$$\frac { \pi }{ 6 } { l }^{ 3 }$$

Subfacets
A sphere has no subfacets of one dimension or below. Its only two-dimensional subfacet is its surface, which is also, quite confusingly, called a sphere. To unambiguously distinguish between the 2D surface and the 3D volume, the volume can be called a "ball".
 * 1 sphere (2D)