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The sphere is a the [[rotatope]] with three round dimensions, and no flat dimensions. Hence, it is the [[Space|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 sphere is a the [[rotatope]] with three round dimensions, and no flat dimensions. Hence, it is the [[Space|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]]. |
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+ | == Equation == |
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+ | A sphere of diameter <math>l</math> can be constructed by drawing the curve that satisfies <math>2\sqrt { 3({ x }^{ 2 }+{ y }^{ 2 }+{ z }^{ 2 }) } ={ l }</math>. |
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* [[vertex count]] = <math>N/A</math> |
* [[vertex count]] = <math>N/A</math> |
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* [[edge length]] = <math>N/A</math> |
* [[edge length]] = <math>N/A</math> |
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* [[surcell volume]] = <math>\frac { \pi }{ 6 } { l }^{ 3 }</math> |
* [[surcell volume]] = <math>\frac { \pi }{ 6 } { l }^{ 3 }</math> |
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− | + | == Subfacets == |
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* 1 [[sphere]] (2D) |
* 1 [[sphere]] (2D) |
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A sphere has no subfacets of one dimension or below. It's 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". |
A sphere has no subfacets of one dimension or below. It's 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". |
Revision as of 19:33, 14 January 2015
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 can be constructed by drawing the curve that satisfies .
Hypervolumes
Subfacets
- 1 sphere (2D)
A sphere has no subfacets of one dimension or below. It's 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 |