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Geometric space with six dimensions
is six-dimensional Euclidean space, in which 6-polytopes and the 5-sphere are constructed. Six-dimensional elliptical space and hyperbolic spaces are
Six-dimensional_space
Property of a mathematical space
case of metric spaces, (n + 1)-dimensional balls have n-dimensional boundaries, permitting an inductive definition based on the dimension of the boundaries
Dimension
Topological space of dimension zero
In mathematics, a zero-dimensional topological space (or nildimensional space) is a topological space that has dimension zero with respect to one of several
Zero-dimensional_space
Space with one dimension
Any straight line or smooth curve is a one-dimensional space, regardless of the dimension of the ambient space in which the line or curve is embedded. Examples
One-dimensional_space
Number of vectors in any basis of the vector space
finite-dimensional if the dimension of V {\displaystyle V} is finite, and infinite-dimensional if its dimension is infinite. The dimension of the vector space V {\displaystyle
Dimension_(vector_space)
Geometric space with seven dimensions
also refer to a seven-dimensional manifold such as a 7-sphere, or a variety of other geometric constructions. Seven-dimensional spaces have a number of special
Seven-dimensional_space
Geometric model of the physical space
3-space. Most commonly, it means the three-dimensional Euclidean space, which is the Euclidean space of dimension three, which models physical space. More
Three-dimensional_space
Mathematical space with two coordinates
A two-dimensional space is a mathematical space with two dimensions, meaning points have two degrees of freedom: their locations can be locally described
Two-dimensional_space
Geometric space with four dimensions
(higher-dimensional analogues of the Platonic solids) that exist in Euclidean spaces of any dimension, including six found in 4-dimensional space. Schläfli's
Four-dimensional_space
Geometric space with five dimensions
five-dimensional spaces include super-dimensional or hyper-dimensional spaces, which generally refer to any space with more than four dimensions. These
Five-dimensional_space
Geometric space with eight dimensions
Eight-dimensional (8D) space is a sequence of n real numbers (when n = 8) that can be understood as a location in n-dimensional space. Often such spaces are
Eight-dimensional_space
Fundamental space of geometry
Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, in Euclid's Elements, it was the three-dimensional space
Euclidean_space
Symmetry group of a configuration in space
the wallpaper groups also apply, or can apply, to three-dimensional arrangements. The space groups that repeat in all three dimensions are classified
Space_group
Topologically invariant definition of the dimension of a space
n exists, the space is said to have infinite covering dimension. As a special case, a non-empty topological space is zero-dimensional with respect to
Lebesgue_covering_dimension
Topics referred to by the same term
abolition of slavery postage stamp, a 1921 stamp issue Six-dimensional space, any space that has six dimensions 6D, the production code for the 1983 Doctor
6D
Topics referred to by the same term
The Sixth Dimension or Sixth Dimension may refer to: Six-dimensional space, a concept in mathematics and physics Sixth Dimension, a 2017 album by Power
The_Sixth_Dimension
Mathematical problem
higher-dimensional spaces that preserve unit distances but are not isometries. For instance, the Euclidean plane can be mapped to a six-dimensional space by
Hadwiger–Nelson_problem
actually tessellates a space of one dimension less. For example, the (three-dimensional) platonic solids tessellate the 'two'-dimensional 'surface' of the sphere
List_of_mathematical_shapes
Four-dimensional analogue of the cube
a tesseract or 4-cube is a four-dimensional hypercube, analogous to a two-dimensional square and a three-dimensional cube. Just as the perimeter of the
Tesseract
Manifold or algebraic variety of dimension n in a space of dimension n+1
variety of dimension n − 1, which is embedded in an ambient space of dimension n, generally a Euclidean space, an affine space or a projective space. Hypersurfaces
Hypersurface
Equation of statistical mechanics
unknown function in the equation is a probability density function in six-dimensional space of a particle position and momentum. The problem of existence and
Boltzmann_equation
Subspace of n-space whose dimension is (n-1)
generalization of a two-dimensional plane in three-dimensional space to mathematical spaces of arbitrary dimension. Like a plane in space, a hyperplane is a
Hyperplane
Invariant measure of fractal dimension
covered) and continuously, so that a one-dimensional object completely fills up a higher-dimensional object. Every space-filling curve hits some points multiple
Hausdorff_dimension
Geometric model of the planar projection of the physical universe
plane is a flat two-dimensional surface that extends indefinitely. Euclidean planes often arise as subspaces of three-dimensional space R 3 {\displaystyle
Euclidean_plane
Method of determining fractal dimension
Bouligand. To calculate this dimension for a fractal S {\textstyle S} , imagine this fractal lying on an evenly spaced grid and count how many boxes
Minkowski–Bouligand_dimension
Science fiction anime series
"Space War I - Macross Compendium". Macross Compendium. Archived from the original on 17 August 2025. Retrieved 13 February 2026. Super Dimension Fortress
Super Dimension Fortress Macross
Super_Dimension_Fortress_Macross
Invariant of topological spaces
that, in n-dimensional Euclidean space Rn, the boundaries of balls have dimension n − 1. Therefore it should be possible to define the dimension of a general
Inductive_dimension
Complex three dimensional gauge theory
physics, six-dimensional holomorphic Chern–Simons theory or sometimes holomorphic Chern–Simons theory is a gauge theory on a three-dimensional complex
Six-dimensional holomorphic Chern–Simons theory
Six-dimensional_holomorphic_Chern–Simons_theory
Completion of the usual space with "points at infinity"
projective space of dimension n ≥ 3 is isomorphic with a PG(n, K), the n-dimensional projective space over some division ring K. A finite projective space is
Projective_space
Solid with six equal square faces
which all six quadrilateral faces are squares. It is a three-dimensional hypercube, a family of polytopes that also includes the two-dimensional square and
Cube
Measure of a mathematical object studied in the field of algebraic geometry
of V. This definition generalizes a property of the dimension of a Euclidean space or a vector space. It is thus probably the definition that gives the
Dimension of an algebraic variety
Dimension_of_an_algebraic_variety
5-simplex honeycomb Truncated 5-simplex honeycomb 5-demicubic honeycomb Six-dimensional space, 6-polytope and uniform 6-polytope 6-simplex, Rectified 6-simplex
List of polygons, polyhedra and polytopes
List_of_polygons,_polyhedra_and_polytopes
Natural number
are generated from four different fundamental Coxeter groups in six-dimensional space. The sum of the first eight Heegner numbers is 153. The Gospel of
153_(number)
Geometric object with flat sides
generalization of three-dimensional polyhedra to any number of dimensions. Polytopes may exist in any general number of dimensions n as an n-dimensional polytope or
Polytope
Types of movement possible for a rigid body in three-dimensional space
mechanical degrees of freedom of movement of a rigid body in three-dimensional space. Specifically, the body is free to change position as forward/backward
Six_degrees_of_freedom
Variants of chess with multiple boards at different levels
Three-dimensional chess (or 3D chess) refers to a family of chess variants that replaces the two-dimensional board with a three-dimensional array of cells
Three-dimensional_chess
Spacetime with complexified coordinates
Wolfgang Pauli generalised the Kaluza–Klein theory to a six-dimensional space, and (using dimensional reduction) derived the essentials of an SU(2) gauge
Complex_spacetime
Geometric representation of material yield
A yield surface is a five-dimensional surface in the six-dimensional space of stresses. The yield surface is usually convex and the state of stress of
Yield_surface
78-dimensional exceptional simple Lie group
span a six-dimensional space, it is much more symmetrical to consider them as vectors in a six-dimensional subspace of a nine-dimensional space. Then one
E6_(mathematics)
Generalized sphere of dimension n (mathematics)
embedding of the 1-dimensional circle is in 2-dimensional space, the 2-dimensional sphere is usually depicted embedded in 3-dimensional space, and a general
N-sphere
Number of independent parameters of a system
used in explaining dependence on parameters, or the dimensions of a phase space Degrees of freedom (statistics), the number of values in the final calculation
Degrees_of_freedom
Fundamental object of geometry
indivisible elements comprising the space, of which one-dimensional curves, two-dimensional surfaces, and higher-dimensional objects consist. In classical Euclidean
Point_(geometry)
Furioso is a fantasy role-playing game adventure published by Dimension Six in 1980. Furioso is an adventure based on part of the epic Orlando Furioso
Furioso_(Dimension_Six)
Framework of superstring theory
eleven-dimensional supergravity. Although a complete formulation of M-theory is not known, such a formulation should describe two- and five-dimensional objects
M-theory
Faster-than-light travel in science fiction
hyperspace was simply a synonym for higher-dimensional space (that is, higher than three dimensional space). This usage was most common in 19th-century
Hyperspace
Geometry and crystallography point array
lattice points. The set of translation operations is described in three dimensional space by R = n 1 a 1 + n 2 a 2 + n 3 a 3 , {\displaystyle \mathbf {R} =n_{1}\mathbf
Bravais_lattice
Four-dimensional number system
mathematics, particularly for calculations involving three-dimensional rotations, such as in three-dimensional computer graphics, computer vision, robotics, magnetic
Quaternion
Real-valued number of spatial dimensions
sets); 1 for sets describing lines (1-dimensional sets having length only); 2 for sets describing surfaces (2-dimensional sets having length and width); and
Fractal_dimension
Polyhedron which tiles 3D space
In geometry, a space-filling polyhedron is a polyhedron that can be used to fill all of three-dimensional space via translations, rotations and/or reflections
Space-filling_polyhedron
Book by John Stephen Roy Chisholm
Vectors in Three-dimensional Space (1978) is a book concerned with physical quantities defined in "ordinary" 3-space. It was written by J. S. R. Chisholm
Vectors in Three-dimensional Space
Vectors_in_Three-dimensional_Space
Board game
Direct Conflict in Dimension Six is a science fiction combat board game published in 1977 by Dimension Six, Inc. Dimension Six is a board game in which
Direct Conflict in Dimension Six
Direct_Conflict_in_Dimension_Six
Solution of Einstein field equations
multilinear operator on the four-dimensional space of tangent vectors (at some event), but a linear operator on the six-dimensional space of bivectors at that event
Gödel_metric
Fictional time-travelling device
The TARDIS (/ˈtɑːr.dɪs/; acronym for "Time And Relative Dimension(s) In Space") is a fictional hybrid of a time machine and spacecraft that has, since
TARDIS
Element of a unital algebra over the field of real numbers
numbers: 2 n {\displaystyle 2^{n}} -dimensional vector spaces over the reals, 2 n − 1 {\displaystyle 2^{n-1}} -dimensional over the complex numbers composition
Hypercomplex_number
Field of mathematics dealing with three-dimensional Euclidean spaces
the geometry of three-dimensional Euclidean space (3D space). A solid figure is the region of 3D space bounded by a two-dimensional closed surface; for
Solid_geometry
Topics referred to by the same term
whose subgroup lattice is modular Iwasawa manifold, a mathematical six-dimensional space Iwasawa Station, railway station Masami Iwasawa (岩沢 まさみ), a character
Iwasawa
Technique in theoretical physics
one of its space-time dimensions. Instead of having a theory with this dimension being infinite, one changes the theory so that this dimension has a finite
Compactification_(physics)
Non-orientable mathematical surface
being contained in four dimensions. By adding a fourth dimension to the three-dimensional space, the self-intersection can be eliminated. Gently push a
Klein_bottle
Mathematical model combining space and time
space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum
Spacetime
Geometric concept
is the maximum possible kissing number for n-dimensional spheres in (n + 1)-dimensional Euclidean space? More unsolved problems in mathematics In geometry
Kissing_number
Curve whose range contains the unit square
In mathematical analysis, a space-filling curve is a curve whose range reaches every point in a higher dimensional region, typically the unit square (or
Space-filling_curve
Role playing game supplement
The Dungeon is a 1980 role-playing game supplement published by Dimension Six. The Dungeon is a set of interchangeable pieces that fit together to construct
The_Dungeon_(Dimension_Six)
Theory of subatomic structure
physics are replaced by one-dimensional objects called strings. String theory describes how these strings move through space and interact with each other
String_theory
In mathematics, dimension of a ring
affine space of dimension n over a field has dimension n, as expected. In general, if R is a Noetherian ring of dimension n, then the dimension of R[x]
Krull_dimension
Sphere tangent to every edge of a polyhedron
tetrahedra"; they form a four-dimensional subfamily of the six-dimensional space of all tetrahedra (as parameterized by their six edge lengths). More precisely
Midsphere
Quaternions with complex number coefficients
commutator, A forms the Lie algebra of G. Thus this study of a six-dimensional space serves to introduce the general concepts of Lie theory. When viewed
Biquaternion
Topological space in group theory
the span of this vector as a one dimensional subspace of Rn, then the complement is an (n − 1)-dimensional vector space that is invariant under an orthogonal
Homogeneous_space
Group of geometric symmetries with at least one fixed point
360. The following table gives the six-dimensional reflection groups (excluding those that are lower-dimensional reflection groups), by listing them
Point_group
Method for producing composition algebras
independent real numbers, they form a two-dimensional vector space over the real numbers. Besides being of higher dimension, the complex numbers can be said to
Cayley–Dickson_construction
Topics referred to by the same term
Look up space in Wiktionary, the free dictionary. Space is a three-dimensional continuum containing positions and directions. Space, SPACE, spacing, or
Space_(disambiguation)
Multi-dimensional generalization of triangle
polytope in any given dimension. For example, a 0-dimensional simplex is a point, a 1-dimensional simplex is a line segment, a 2-dimensional simplex is a triangle
Simplex
Topological space that locally resembles Euclidean space
is a topological space that locally resembles Euclidean space near each point. More precisely, an n {\displaystyle n} -dimensional manifold, or n {\displaystyle
Manifold
Solid with four equal triangular faces
honeycomb. The pentachoron is a four-dimensional polytope, a generalization of a tetrahedron in four-dimensional space. It is bounded by five regular tetrahedra
Regular_tetrahedron
Convex polytope, the n-dimensional analogue of a square and a cube
{\displaystyle {\sqrt {n}}} . An n-dimensional hypercube is more commonly referred to as an n-cube or sometimes as an n-dimensional cube. The term measure polytope
Hypercube
Method of assigning coordinates to every line in projective 3-space
(projective 5-space). A predecessor and special case of Grassmann coordinates (which describe k-dimensional linear subspaces, or flats, in an n-dimensional Euclidean
Plücker_coordinates
1968 film by Stanley Kubrick
2001: A Space Odyssey is a 1968 epic science fiction film produced and directed by Stanley Kubrick, who co-wrote the screenplay with Arthur C. Clarke
2001:_A_Space_Odyssey
Set of mathematical concepts in quantum gravity
intuition. Generally, string theory is initially explored on a compact six-dimensional manifold to restrict the algebraic data needed for computation. By
Quantum_geometry
2025 Internet meme and slang term
6-7 (pronounced "six seven"; also written as 67 or 6 7) is an Internet meme, slang term, and gesture that became popular in late 2025 on TikTok and Instagram
6-7
Natural number
to the two-dimensional kissing number problem. A cube has 6 faces. A tetrahedron has 6 edges. In four dimensions, there are a total of six convex regular
6
This three-dimensional example was later proven to be optimal, and to be the unique optimal solution. Kelly's eight-point three-dimensional isosceles set
Isosceles_set
Non-orientable surface with one edge
Möbius strip. As an abstract topological space, the Möbius strip can be embedded into three-dimensional Euclidean space in many different ways: A clockwise
Möbius_strip
Four-dimensional analogues of the regular polyhedra in three dimensions
4-polytope or regular polychoron is a regular four-dimensional polytope. They are the four-dimensional analogues of the regular polyhedra in three dimensions
Regular_4-polytope
Natural number
roots of −1, seven-dimensional vectors have a cross product, and the number of equiangular lines possible in seven-dimensional space is anomalously large
7
Classification used in differential geometry and general relativity
{C^{ab}}_{mn}\,X^{mn}=\lambda \,X^{ab}} In (four-dimensional) Lorentzian spacetimes, there is a six-dimensional space of antisymmetric bivectors at each event
Petrov_classification
defined by the dimensional cross is the Octahedron. Laban devised movement scales that follow these three dimensions, called the Dimensional Scales. Two
Space_Harmony
4-D convex polytope
radii. The tesseract tessellates four-dimensional space as the tesseractic honeycomb.[citation needed] The 4-dimensional content of a unit-edge-length tesseract
Cubic_pyramid
Broad concept generalizing scalars in mathematics and physics
dimension is an infinite cardinal. Finite-dimensional vector spaces occur naturally in geometry and related areas. Infinite-dimensional vector spaces
Vector (mathematics and physics)
Vector_(mathematics_and_physics)
N-dimensional generalisation of a pyramid
called a n-dimensional hyperpyramid. A normal triangle is a 2-dimensional hyperpyramid, the tetrahedron or triangular pyramid is a 3-dimensional hyperpyramid
Hyperpyramid
Aperiodic tile
suggest a three-dimensional analogue to the monotile. Taylor and Socolar remark that the 3D monotile aperiodically tiles three-dimensional space. However the
Socolar–Taylor_tile
Three-dimensional fractal
Sierpiński sponge) is a fractal curve. It is a three-dimensional generalization of the two-dimensional Sierpinski carpet. It was first described by Karl
Menger_sponge
Generalization of a rectangle for higher dimensions
of the set of all 3-cells. A four-dimensional orthotope is likely a hypercuboid. The special case of an n-dimensional orthotope where all edges have equal
Hyperrectangle
Four-dimensional analogue of the tetrahedron
from all the vertices of the tetrahedron. This cannot be done in 3-dimensional space. The regular 5-cell is a solution to the problem: Make 10 equilateral
5-cell
Vector representing the position of a point with respect to a fixed origin
used in two-dimensional or three-dimensional space, but can be easily generalized to Euclidean spaces and affine spaces of any dimension. The relative
Position_(geometry)
Geometric system with a finite number of points
geometry of higher-dimensional finite spaces, see axiomatic projective space. For a discussion of higher-dimensional finite spaces in general, see, for
Finite_geometry
Motion of a certain space that preserves at least one point
reflections, each of them having an entire (n − 1)-dimensional flat of fixed points in a n-dimensional space. Mathematically, a rotation is a map. All rotations
Rotation_(mathematics)
6-dimensional hypercube
In geometry, a 6-cube is a six-dimensional hypercube with 64 vertices, 192 edges, 240 square faces, 160 cubic cells, 60 tesseract 4-faces, and 12 5-cube
6-cube
Planar surface that forms part of the boundary of a solid object
For example, a cube has six faces in this sense. In more modern treatments of the geometry of polyhedra and higher-dimensional polytopes, a "face" is defined
Face_(geometry)
Method for specifying point positions
coordinate hypersurfaces are the (n − 1)-dimensional spaces resulting from fixing a single coordinate of an n-dimensional coordinate system. The concept of a
Coordinate_system
6-dimensional geometric object
In six-dimensional geometry, a six-dimensional polytope or 6-polytope is a polytope, bounded by 5-polytope facets. A 6-polytope is a closed six-dimensional
6-polytope
Polyhedron with eight triangular faces
axis-parallel unit vectors in three-dimensional Euclidean space. It is one of the five Platonic solids, and the three-dimensional case of an infinite family of
Octahedron
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SIX DIMENSIONAL-SPACE
SIX DIMENSIONAL-SPACE
SIX DIMENSIONAL-SPACE
SIX DIMENSIONAL-SPACE
SIX DIMENSIONAL-SPACE
SIX DIMENSIONAL-SPACE
SIX DIMENSIONAL-SPACE
SIX DIMENSIONAL-SPACE
SIX DIMENSIONAL-SPACE
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