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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

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 Eleventh Twelfth Thirteenth Fourteenth Fifteenth Sixteenth
Simplex Point Line Triangle Tetrahedron Pentachoron Hexateron Heptapeton Octaexon Enneazetton Decayotton Hendecaxennon Dodecadakon Tredecahendakon Quattuordecadokon Quindecatradakon Sexdecateradakon Septendecapetadakon
Hypercube Point Line Square Cube Tesseract Penteract Hexeract Hepteract Octeract Enneract Dekeract Undekeract Dodekeract Tredekeract Quattuordekeract Quindekeract Sexdekeract
Cross Point Line Square Octahedron Hexadecachoron Pentarss Hexarss Heptarss Octarss Ennearss Decarss Hendecarss Dodecarss Tredecarss Quattuordecarss Quindecatrarss Sexdecaterarss
Hypersphere Point Line Circle Sphere Glome Hyperglome Hexaphere Heptaphere Octaphere Enneaphere Decaphere Hendecaphere Dodecaphere Tredecaphere Quattuordecaphere Quindecatraphere Sexdecateraphere
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