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.

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

• 1 sphere (2D)

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".

See also

	Zeroth	First	Second	Third	Fourth	Fifth	Sixth	Seventh	Eighth	Ninth	Tenth
Simplex	Point	Line	Triangle	Tetrahedron	Pentachoron	Hexateron	Heptapeton	Octaexon	Enneazetton	Decayotton	Hendecaxennon
Hypercube	Point	Line	Square	Cube	Tesseract	Penteract	Hexeract	Hepteract	Octeract	Enneract	Dekeract
Cross	Point	Line	Square	Octahedron	Hexadecachoron	Pentarss	Hexarss	Heptarss	Octarss	Ennearss	Decarss
Hypersphere	Point	Line	Circle	Sphere	Glome	Hyperglome	Hexaphere	Heptaphere	Octaphere	Enneaphere	Decaphere