Point

A point is a position, with a size equal to 0. This does not mean an entire region however. It is defined by Euclid as "that which has no part", which is an apt description - a point has no height, width, depth, or any other measure in any other dimension.

Furthermore, a point can also be thought of as a 'dimensionless' coordinate, meaning a coordinate without a definite numerical or algebraic value.

It is also the only zero dimensional shape, and any zero-dimensional space consists of a single point and nothing else. This means that it can be considered as a zero-dimensional space of infinite extent, in analogue with the plane.

A line can be thought of as consisting of an uncountably infinite amount of points placed directly adjacent to each other in the same direction.

Likewise, a plane can be thought of as consisting of an infinite amount of parallel lines that are infinitely close.

The point represents the idea of unity in many religions and ethnic groups.

Structure and Sections[]

Hypervolumes[]

vertex count = $1$

Subfacets[]

1 null polytope (-1D)
1 point (0D)

Notations[]

Toratopic notation: $.$
Tapertopic notation: 0

Related shapes[]

Dual: Self-dual
Vertex figure: Null polytope

See also[]

Dimensionality	Negative One	Zero	One	Two	Three	Four	Five	Six	Seven	Eight	Nine	Ten	Eleven	Twelve	Thirteen	Fourteen	Fifteen	Sixteen	Seventeen	...	Aleph null
Simplex $\{3^{n-1}\}$	Null polytope $)($ $\emptyset$	Point $()$ $\mathbb{B}^0$	Line segment $\{\}$ $\mathbb{B}^1$	Triangle $\{3\}$	Tetrahedron $\{3^2\}$	Pentachoron $\{3^3\}$	Hexateron $\{3^4\}$	Heptapeton $\{3^5\}$	Octaexon $\{3^6\}$	Enneazetton $\{3^7\}$	Decayotton $\{3^8\}$	Hendecaxennon $\{3^9\}$	Dodecadakon $\{3^{10}\}$	Tridecahendon $\{3^{11}\}$	Tetradecadokon $\{3^{12}\}$	Pentadecatradakon $\{3^{13}\}$	Hexadecatedakon $\{3^{14}\}$	Heptadecapedakon $\{3^{15}\}$	Octadecapedakon $\{3^{16}\}$	...	Omegasimplex
Cross $\{3^{n-2},4\}$				Square $\{4\}$	Octahedron $\{3, 4\}$	Hexadecachoron $\{3^2, 4\}$	Pentacross $\{3^3, 4\}$	Hexacross $\{3^4, 4\}$	Heptacross $\{3^5, 4\}$	Octacross $\{3^6, 4\}$	Enneacross $\{3^7, 4\}$	Dekacross $\{3^8, 4\}$	Hendekacross $\{3^9, 4\}$	Dodekacross $\{3^{10}, 4\}$	Tridekacross $\{3^{11}, 4\}$	Tetradekacross $\{3^{12}, 4\}$	Pentadekacross $\{3^{13}, 4\}$	Hexadekacross $\{3^{14}, 4\}$	Heptadekacross $\{3^{15}, 4\}$	...	Omegacross
Hydrotopes $\{3^{n-2}, 5\}$				Pentagon $\{5\}$	Icosahedron $\{3, 5\}$	Hexacosichoron $\{3^2, 5\}$	Order-5 pentachoric tetracomb $\{3^3, 5\}$	Order-5 hexateric pentacomb $\{3^4, 5\}$	...
Hypercube $\{4, 3^{n-2}\}$				Square $\{4\}$	Cube $\{4, 3\}$	Tesseract $\{4, 3^2\}$	Penteract $\{4, 3^3\}$	Hexeract $\{4, 3^4\}$	Hepteract $\{4, 3^5\}$	Octeract $\{4, 3^6\}$	Enneract $\{4, 3^7\}$	Dekeract $\{4, 3^8\}$	Hendekeract $\{4, 3^9\}$	Dodekeract $\{4, 3^{10}\}$	Tridekeract $\{4, 3^{11}\}$	Tetradekeract $\{4, 3^{12}\}$	Pentadekeract $\{4, 3^{13}\}$	Hexadekeract $\{4, 3^{14}\}$	Heptadekeract $\{4, 3^{15}\}$	...	Omegeract
Cosmotopes $\{5, 3^{n-2}\}$				Pentagon $\{5\}$	Dodecahedron $\{5, 3\}$	Hecatonicosachoron $\{5, 3^2\}$	Order-3 hecatonicosachoric tetracomb $\{5, 3^3\}$	Order-3-3 hecatonicosachoric pentacomb $\{5, 3^4\}$	...
Hyperball $\mathbb B^n$				Disk $\mathbb B^2$	Ball $\mathbb B^3$	Gongol $\mathbb B^4$	Pentorb $\mathbb B^5$	Hexorb $\mathbb B^6$	Heptorb $\mathbb B^7$	Octorb $\mathbb B^8$	Enneorb $\mathbb B^9$	Dekorb $\mathbb B^{10}$	Hendekorb $\mathbb B^{11}$	Dodekorb $\mathbb B^{12}$	Tridekorb $\mathbb B^{13}$	Tetradekorb $\mathbb B^{14}$	Pentadekorb $\mathbb B^{15}$	Hexadekorb $\mathbb B^{16}$	Heptadekorb $\mathbb B^{17}$	...	Omegaball $\mathbb B^{\aleph_0}$

Dimensionality	Negative One	Zero	One	Two	Three	Four	Five	Six	Seven	Eight	Nine	Ten	...	Aleph null
Hyperbolic space $\mathbb H^{n}$	—	—	—	Hyperbolic plane $\mathbb H^{2}$	Hyperbolic realm $\mathbb H^{3}$	Hyperbolic flune $\mathbb H^{4}$	Hyperbolic pentrealm $\mathbb H^{5}$	Hyperbolic hexealm $\mathbb H^{6}$	Hyperbolic heptealm $\mathbb H^{7}$	Hyperbolic octealm $\mathbb H^{8}$	Hyperbolic ennealm $\mathbb H^{9}$	Hyperbolic decealm $\mathbb H^{10}$	...	Hyperbolic omegealm $\mathbb H^{\aleph_0}$
Euclidean space $\R^n$	Null polytope $\emptyset$	Point $\mathbb R^{0}$	Euclidean line $\mathbb R^{1}$	Euclidean plane $\mathbb R^{2}$	Euclidean realm $\mathbb R^{3}$	Euclidean flune $\mathbb R^{4}$	Euclidean pentrealm $\mathbb R^{5}$	Euclidean hexealm $\mathbb R^{6}$	Euclidean heptealm $\mathbb R^{7}$	Euclidean octealm $\mathbb R^{8}$	Euclidean ennealm $\mathbb R^{9}$	Euclidean decealm $\mathbb R^{10}$	...	Euclidean omegealm $\mathbb R^{\aleph_0}$
Hypersphere $\mathbb S^{n}$	Null polytope $\emptyset$	Point pair $\mathbb S^{0}$	Circle $\mathbb S^{1}$	Sphere $\mathbb S^{2}$	Glome $\mathbb S^{3}$	Tetrasphere $\mathbb S^{4}$	Pentasphere $\mathbb S^{5}$	Hexasphere $\mathbb S^{6}$	Heptasphere $\mathbb S^{7}$	Octasphere $\mathbb S^{8}$	Enneasphere $\mathbb S^{9}$	Dekasphere $\mathbb S^{10}$	...	Omegasphere $\mathbb S^{\aleph_0}$

Dimensionality	Negative One	Zero	One	Two	Three	Four	Five	Six	Seven	Eight	Nine	Ten	Eleven	Twelve	Thirteen	Fourteen	Fifteen	Sixteen	Seventeen	...	Aleph null
Simplex \(\{3^{n-1}\}\)	Null polytope \()(\) \(\emptyset\)	Point \(()\) \(\mathbb{B}^0\)	Line segment \(\{\}\) \(\mathbb{B}^1\)	Triangle \(\{3\}\)	Tetrahedron \(\{3^2\}\)	Pentachoron \(\{3^3\}\)	Hexateron \(\{3^4\}\)	Heptapeton \(\{3^5\}\)	Octaexon \(\{3^6\}\)	Enneazetton \(\{3^7\}\)	Decayotton \(\{3^8\}\)	Hendecaxennon \(\{3^9\}\)	Dodecadakon \(\{3^{10}\}\)	Tridecahendon \(\{3^{11}\}\)	Tetradecadokon \(\{3^{12}\}\)	Pentadecatradakon \(\{3^{13}\}\)	Hexadecatedakon \(\{3^{14}\}\)	Heptadecapedakon \(\{3^{15}\}\)	Octadecapedakon \(\{3^{16}\}\)	...	Omegasimplex
Cross \(\{3^{n-2},4\}\)				Square \(\{4\}\)	Octahedron \(\{3, 4\}\)	Hexadecachoron \(\{3^2, 4\}\)	Pentacross \(\{3^3, 4\}\)	Hexacross \(\{3^4, 4\}\)	Heptacross \(\{3^5, 4\}\)	Octacross \(\{3^6, 4\}\)	Enneacross \(\{3^7, 4\}\)	Dekacross \(\{3^8, 4\}\)	Hendekacross \(\{3^9, 4\}\)	Dodekacross \(\{3^{10}, 4\}\)	Tridekacross \(\{3^{11}, 4\}\)	Tetradekacross \(\{3^{12}, 4\}\)	Pentadekacross \(\{3^{13}, 4\}\)	Hexadekacross \(\{3^{14}, 4\}\)	Heptadekacross \(\{3^{15}, 4\}\)	...	Omegacross
Hydrotopes \(\{3^{n-2}, 5\}\)				Pentagon \(\{5\}\)	Icosahedron \(\{3, 5\}\)	Hexacosichoron \(\{3^2, 5\}\)	Order-5 pentachoric tetracomb \(\{3^3, 5\}\)	Order-5 hexateric pentacomb \(\{3^4, 5\}\)	...
Hypercube \(\{4, 3^{n-2}\}\)				Square \(\{4\}\)	Cube \(\{4, 3\}\)	Tesseract \(\{4, 3^2\}\)	Penteract \(\{4, 3^3\}\)	Hexeract \(\{4, 3^4\}\)	Hepteract \(\{4, 3^5\}\)	Octeract \(\{4, 3^6\}\)	Enneract \(\{4, 3^7\}\)	Dekeract \(\{4, 3^8\}\)	Hendekeract \(\{4, 3^9\}\)	Dodekeract \(\{4, 3^{10}\}\)	Tridekeract \(\{4, 3^{11}\}\)	Tetradekeract \(\{4, 3^{12}\}\)	Pentadekeract \(\{4, 3^{13}\}\)	Hexadekeract \(\{4, 3^{14}\}\)	Heptadekeract \(\{4, 3^{15}\}\)	...	Omegeract
Cosmotopes \(\{5, 3^{n-2}\}\)				Pentagon \(\{5\}\)	Dodecahedron \(\{5, 3\}\)	Hecatonicosachoron \(\{5, 3^2\}\)	Order-3 hecatonicosachoric tetracomb \(\{5, 3^3\}\)	Order-3-3 hecatonicosachoric pentacomb \(\{5, 3^4\}\)	...
Hyperball \(\mathbb B^n\)				Disk \(\mathbb B^2\)	Ball \(\mathbb B^3\)	Gongol \(\mathbb B^4\)	Pentorb \(\mathbb B^5\)	Hexorb \(\mathbb B^6\)	Heptorb \(\mathbb B^7\)	Octorb \(\mathbb B^8\)	Enneorb \(\mathbb B^9\)	Dekorb \(\mathbb B^{10}\)	Hendekorb \(\mathbb B^{11}\)	Dodekorb \(\mathbb B^{12}\)	Tridekorb \(\mathbb B^{13}\)	Tetradekorb \(\mathbb B^{14}\)	Pentadekorb \(\mathbb B^{15}\)	Hexadekorb \(\mathbb B^{16}\)	Heptadekorb \(\mathbb B^{17}\)	...	Omegaball \(\mathbb B^{\aleph_0}\)