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Convex polytope, the n-dimensional analogue of a square and a cube
In geometry, a hypercube is an n-dimensional analogue of a square (n = 2) and a cube (n = 3); the special case for n = 4 is known as a tesseract. It is
Hypercube
Graphs formed by a hypercube's edges and vertices
In graph theory, the hypercube graph Q n {\displaystyle Q_{n}} is the edge graph of the n {\displaystyle n} -dimensional hypercube, that is, it is the
Hypercube_graph
Topics referred to by the same term
A hypercube is a convex polytope, the n-dimensional analogue of a square and a cube. It may also refer to: Cube 2: Hypercube, a film Tesseract, a four-dimensional
Hypercube_(disambiguation)
2002 film by Andrzej Sekula
Cube 2: Hypercube (stylized on-screen as Cube²: Hypercube) is a 2002 Canadian science fiction horror film directed by Andrzej Sekuła, written by Sean
Cube_2:_Hypercube
Four-dimensional analogue of the cube
In geometry, 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
Tesseract
Generalization of a magic square
In mathematics, a magic hypercube is the k-dimensional generalization of magic squares and magic cubes, that is, an n × n × n × ... × n array of integers
Magic_hypercube
Statistical sampling technique
Latin hypercube sampling (LHS) is a statistical method for generating a near-random sample of parameter values from a multidimensional distribution. The
Latin_hypercube_sampling
Canadian science-fiction horror film series
following, with critics praising its minimalist setting and tension. Cube 2: Hypercube is a sequel to the film Cube. The dusky, dingy rooms of the first film
Cube_(film_series)
Type of network topology
networking, hypercube networks are a type of network topology used to connect and route data between multiple processing units or computers. Hypercube networks
Hypercube internetwork topology
Hypercube_internetwork_topology
1954 painting by Salvador Dalí
the Crucifixion, it depicts Christ on a polyhedron net of a tesseract (hypercube). It is one of his best-known paintings from the later period of his career
Crucifixion (Corpus Hypercubus)
Crucifixion_(Corpus_Hypercubus)
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
Computing technique employed to achieve parallelism
extended, or hierarchical type. Distributed memory machines may have hypercube or mesh interconnection schemes. An example of MIMD system is Intel Xeon
Multiple instruction, multiple data
Multiple_instruction,_multiple_data
Cube with edge length one
surface area is 6 square units. The term unit cube or unit hypercube is also used for hypercubes, or "cubes" in n-dimensional spaces, for values of n other
Unit_cube
5-dimensional hypercube
five-dimensional geometry, a 5-cube (or penteract) is a five-dimensional hypercube with 32 vertices, 80 edges, 80 square faces, 40 cubic cells, and 10 tesseract
5-cube
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
d {\displaystyle d} -dimensional hypercube is a network topology for parallel computers with 2 d {\displaystyle 2^{d}} processing elements. The topology
Hypercube (communication pattern)
Hypercube_(communication_pattern)
Episode of British TV's Doctor Who
"The Doctor's Wife" is the fourth episode of the sixth series of the British science fiction television series Doctor Who, which was broadcast on 14 May
The_Doctor's_Wife
Canadian actress
on Covert Affairs, Kate Filmore in the science fiction movie Cube 2: Hypercube, and U.S. president Michelle Travers on The Night Agent. She has also
Kari_Matchett
2016 video game
on 15 reviews. "IndieGames.com - The Weblog Freeware Game Pick: Super Hypercube (Kokoromi)". indiegames.com. November 21, 2008. Retrieved October 12,
SuperHyperCube
Shape with four equal sides and angles
regular polytopes that includes the cube in three dimensions and the hypercubes in higher dimensions, and to another family that includes the regular
Square
Multi-dimensional generalization of triangle
labeled as βn, and the hypercubes, labeled as γn. A fourth family, the tessellation of n-dimensional space by infinitely many hypercubes, he labeled as δn
Simplex
Type of sequence in numerical analysis
coordinates in each dimension. Let Is = [0,1]s be the s-dimensional unit hypercube, and f a real integrable function over Is. The original motivation of
Sobol_sequence
Polytope constructed from alternation of a hypercube
n-polytopes constructed from alternation of an n-hypercube, labeled as hγn for being half of the hypercube family, γn. Half of the vertices are deleted and
Demihypercube
Fundamental combinatorial result of Ramsey theory
of the hypercube W8 3 is a string of eight numbers from 1 to 3, e.g. 13211321 is an element of the hypercube. We are assuming that this hypercube is completely
Hales–Jewett_theorem
Geometric space with five dimensions
dimensions. 5-cube — also called a penteract, a specific five-dimensional hypercube. Hypersphere — the generalization of a sphere to higher dimensions, including
Five-dimensional_space
Shape made from cubes joined together
remaining 17 pentacubes has 24 orientations. The tesseract (four-dimensional hypercube) has eight cubes as its facets, and just as the cube can be unfolded into
Polycube
Generative encoding that evolves artificial neural networks
Hypercube-based NEAT, or HyperNEAT, is a generative encoding that evolves artificial neural networks (ANNs) with the principles of the widely used NeuroEvolution
HyperNEAT
Russian architect
“urban supergraphics”. Hypercube is the first building at the Skolkovo Innovation Center. The decision to erect the Hypercube building was made by Russian
Boris_Bernaskoni
Algebraic structure modeling logical operations
Morgan's laws Forcing (mathematics) Free Boolean algebra Heyting algebra Hypercube graph Karnaugh map Laws of Form Logic gate Logical graph Logical matrix
Boolean_algebra_(structure)
Collective operation in parallel computing
achieved simultaneously. Depending on the network topology (fully connected, hypercube, ring), different all-to-all algorithms are required. We consider a single-ported
All-to-all_(parallel_pattern)
Type of network topology
dimension of a toroidal network is 2, the resulting network is called a hypercube. A parallel computing cluster or multi-core processor is often connected
Grid_network
2026 video game
objects they can pick up to furnish their home. The Four Dimensional Hypercube, an intelligent computer and friend to the raccoon, opens portals to more
Funi_Raccoon_Game
Boolean function whose output depends only on the number of true inputs
In mathematics, a symmetric Boolean function is a Boolean function whose value does not depend on the order of its input bits, i.e., it depends only on
Symmetric_Boolean_function
Ranking system for men's and women's national teams in volleyball
year World League: included for 1 year In 2019, FIVB collaborated with Hypercube Business Innovation of the Netherlands to design a new world ranking platform
FIVB_Senior_World_Rankings
Generalization of a rectangle for higher dimensions
{\displaystyle k} -cell is compact. If all of the edges are equal length, it is a hypercube. A hyperrectangle is a special case of a parallelotope. For every integer
Hyperrectangle
Sequence in computer science
and Steele algorithm can be used to accelerate the second phase. The Hypercube Prefix Sum Algorithm is well adapted for distributed memory platforms
Prefix_sum
Quantum algorithm
step. This is an example of how to apply the quantum walk search on a hypercube graph. Although in the original description Szegedy quantum walks are
Quantum_walk_search
Website providing torrent files and magnet links
move from Hypercube to Opentracker as its BitTorrent tracking software, also enabling the use of the UDP tracker protocol for which Hypercube lacked support
The_Pirate_Bay
Pentagram Regular polygon Equilateral triangle Simplex Square Cross-polytope Hypercube Pentagon Hexagon Heptagon Octagon Enneagon Decagon Hendecagon Dodecagon
List_of_mathematical_shapes
Line of computers in the 1980s and 1990s
corners of hypercubes of increasing dimension. Intel announced the iPSC/1 in 1985, with 32 to 128 nodes connected with Ethernet into a hypercube. The system
Intel_iPSC
Concept in mathematical optimisation
The rule was proposed 1979 by W. H. Cunningham to defeat the deformed hypercube constructions by Klee and Minty et al. (see, e.g. Klee–Minty cube). Cunningham's
Cunningham's_rule
Space formed by the ''n''-tuples of real numbers
visualize any affine coordinate system in a real n-space. Vertices of a hypercube have coordinates (x1, x2, ..., xn) where each xk takes on one of only
Real_coordinate_space
Isometric subgraph of a hypercube
is an isometric subgraph of a hypercube. In other words, a partial cube can be identified with a subgraph of a hypercube in such a way that the distance
Partial_cube
Undirected graph derived from a hypercube graph
undirected graph formed from a hypercube graph by adding to it a perfect matching that connects opposite pairs of hypercube vertices. The folded cube graph
Folded_cube_graph
Construction for n-dimensional noise functions
-dimensional triangles). This reduces the number of data points. While a hypercube in n {\displaystyle n} dimensions has 2 n {\displaystyle 2^{n}} corners
Simplex_noise
Film director and producer
perhaps best known as co-producer of the films American Psycho 2, Cube 2: Hypercube, Prisoner of Love, The First 9½ Weeks and The Cat's Meow. Barbarash also
Ernie_Barbarash
Computational problem in graph theory
mathematics What is the maximum length of a snake for each n-dimensional hypercube graph? More unsolved problems in mathematics The snake-in-the-box problem
Snake-in-the-box
Family of regular honeycombs in geometry
group Rn (or B~n−1) for n ≥ 3. The tessellation is constructed from 4 n-hypercubes per ridge. The vertex figure is a cross-polytope {3...3,4}. The hypercubic
Hypercubic_honeycomb
Volleyball ranking system
usually employed is the serpentine system. In 2019, FIVB collaborated with Hypercube Business Innovation of the Netherlands to design a new world ranking platform
FIVB Senior Continental Rankings
FIVB_Senior_Continental_Rankings
Canadian actress (born 1987)
Away From Her, Slings & Arrows, Odd Squad, House Party, and Cube 2: Hypercube. On stage, she has performed The Vagina Monologues in Oranjestad, Aruba
Grace_Lynn_Kung
Parallel computer
Charles Seitz and Geoffrey C Fox from 1981 onward. It was the first working hypercube built. It was an early attempt to capitalise on VLSI to speed up scientific
Caltech_Cosmic_Cube
Product of an integer with itself
triangular numbers Tesseractic numbers Higher dimensional non-centered 5-hypercube numbers 6-hypercube numbers 7-hypercube numbers 8-hypercube numbers
Square_number
Database management system
Japanese, as well as the support of data warehouse functions ("Transbase Hypercube") and the dynamic, parallel execution of queries. Transbase supports all
Transbase
Graph of the vertices and edges of a demihypercube
distance exactly two from each other in the hypercube graph. That is, it is the half-square of the hypercube. This connectivity pattern produces two isomorphic
Halved_cube_graph
Data used to detect errors in other data
m-dimensional hypercube. The effect of a checksum algorithm that yields an n-bit checksum is to map each m-bit message to a corner of a larger hypercube, with
Checksum
Function returning one of only two values
the one bits of m. When the domain is restricted to the n-dimensional hypercube [ 0 , 1 ] n {\displaystyle [0,1]^{n}} , the polynomial f ∗ ( x ) : [ 0
Boolean_function
Assignment of colors to graph vertices that destroys all symmetries
adjacent block lengths. Hypercube graphs exhibit a similar phenomenon to cycle graphs. The two- and three-dimensional hypercube graphs (the 4-cycle and
Distinguishing_coloring
Manifold or algebraic variety of dimension n in a space of dimension n+1
Fractal Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid
Hypersurface
Graph path which is an induced subgraph
sometimes called a snake, and the problem of finding long induced paths in hypercube graphs is known as the snake-in-the-box problem. Similarly, an induced
Induced_path
Polytope with highest degree of symmetry
dimension, the line segment simultaneously serves as the 1-simplex, the 1-hypercube and the 1-orthoplex. In two dimensions, there are infinitely many regular
Regular_polytope
Polish cinematographer and film director (born 1954)
debut with the 1998 thriller Fait Accompli. He then directed Cube 2: Hypercube and The Pleasure Drivers. Feature film "Andrzej Sekula | Cinematographer
Andrzej_Sekuła
Geometric graph with unit edge lengths
include the cactus graphs, the matchstick graphs and penny graphs, and the hypercube graphs. The generalized Petersen graphs are non-strict unit distance graphs
Unit_distance_graph
Undirected cubic graph derived from a hypercube graph
cycles is an undirected cubic graph, formed by replacing each vertex of a hypercube graph by a cycle. It was introduced by Preparata & Vuillemin (1981) for
Cube-connected_cycles
Family of graphs based on the Fibonacci sequence
from its origin in number theory. Mathematically they are similar to the hypercube graphs, but with a Fibonacci number of vertices. Fibonacci cubes were
Fibonacci_cube
Mathematical space with two coordinates
circle Cylinder Cone Four - other-dimensional 4-polytope Simplex 5-cell Hypercube Tesseract n-sphere Geometers by name Aida Aryabhata Ahmes Alhazen Apollonius
Two-dimensional_space
Figurate number
triangular numbers Tesseractic numbers Higher dimensional non-centered 5-hypercube numbers 6-hypercube numbers 7-hypercube numbers 8-hypercube numbers
Triangular_number
Concept in distributed computing
introduced for dealing with presence of faulty links in the network. A Hypercube H k {\displaystyle H_{k}} is a network consisting of n = 2 k {\displaystyle
Leader_election
Mathematical concept
that twist and turn enough to fill the whole of any square, or cube, or hypercube, or finite-dimensional space. These curves can be used to define a one-to-one
Infinity
Family of regular tessellations in geometry
the alternated hypercube honeycomb (or demicubic honeycomb) is a dimensional infinite series of honeycombs, based on the hypercube honeycomb with an
Alternated hypercubic honeycomb
Alternated_hypercubic_honeycomb
Network topology for parallel computers
compares the butterfly network with linear array, ring, 2-D mesh and hypercube networks. Linear array can be considered as a 1-D mesh topology. Relevant
Butterfly_network
Property of a mathematical space
circle Cylinder Cone Four - other-dimensional 4-polytope Simplex 5-cell Hypercube Tesseract n-sphere Geometers by name Aida Aryabhata Ahmes Alhazen Apollonius
Dimension
Categories of number cubes
classification is that it is consistent for all orders and all dimensions of magic hypercubes. Simple: The minimum requirements for a magic cube are: all rows, columns
Magic_cube_classes
Canadian actor, comedian, writer and motivational speaker (born 1960)
Fred Tupper in Little Mosque on the Prairie, Jerry Whitehall in Cube 2: Hypercube and the voices of Gordon, Diesel 10 and Splatter in Thomas and the Magic
Neil_Crone
Type of mathematical array
Latin squares were generalized to Latin cubes and hypercubes, and orthogonal Latin cubes and hypercubes by Kishen (1942). Rao (1946) generalized these results
Orthogonal_array
Minkowsi sum of line segments
{\displaystyle \mathbb {R} ^{d}} or, equivalently as a projection of a hypercube. Zonotopes are intimately connected to hyperplane arrangements and matroid
Zonotope
3D scenery generator software
landscapes." It was published by Virtual Reality Labs and developed by Hypercube Engineering. The latest versions were published and developed by Monkey
VistaPro
N-dimensional generalisation of a pyramid
Fractal Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid
Hyperpyramid
Part of a straight line that is bounded by two distinct end points
simplex is a triangle. A line segment is a one-dimensional hypercube; a two-dimensional hypercube is a square. Chord (geometry) Diameter Radius Polygonal
Line_segment
Geometric inequality applicable to any closed curve
isoperimetric inequalities for the Boolean hypercube. The edge isoperimetric inequality of the hypercube is Φ E ( Q d , k ) ≥ k ( d − log 2 k ) {\displaystyle
Isoperimetric_inequality
Regular polytope dual to the hypercube in any number of dimensions
(n−1)-orthoplex base. The cross-polytope is the dual polytope of the hypercube. The vertex-edge graph of an n-dimensional cross-polytope is the Turán
Cross-polytope
Form of global sensitivity analysis
the inputs are independently and uniformly distributed within the unit hypercube, i.e. X i ∈ [ 0 , 1 ] {\displaystyle X_{i}\in [0,1]} for i = 1 , 2 ,
Variance-based sensitivity analysis
Variance-based_sensitivity_analysis
Convex polyhedron with six faces with four edges each
objects". There exist quadrilateral-faced hexahedra which are non-convex. Hypercube Lists of shapes Robertson, Stewart A. (1984). Polytopes and Symmetry.
Cuboid
Problem easily dividable into parallel tasks
T. (ed.). Hypercube Multiprocessors. Society for Industrial and Applied Mathematics, Philadelphia. ISBN 978-0898712094. The Intel hypercube part 2 reposted
Embarrassingly_parallel
Supercomputer model (produced 1986–1991)
become the CM-1 Connection Machine, a design for a massively parallel hypercube-based arrangement of thousands of microprocessors, springing from his
Connection_Machine
One of two different regular graphs with 16 vertices
between opposite pairs of vertices in a 4-dimensional hypercube graph. (In an n-dimensional hypercube, a pair of vertices are opposite if the shortest path
Clebsch_graph
Mathematical model
fitness, with redder values having higher fitness. The embedding of the hypercube is chosen so that the fitness maximum is at the centre. Notice that the
NK_model
Film by Vincenzo Natali
film of the preceding 15 years. Cube was followed by a sequel, Cube 2: Hypercube, released in 2002. A prequel, Cube Zero, released in 2004. In April 2015
Cube_(1997_film)
regular, with Schläfli symbol {4,36,4}. Another form has two alternating hypercube facets (like a checkerboard) with Schläfli symbol {4,35,31,1}. The lowest
8-cubic_honeycomb
Result of multiplying four instances of a number together
they are squares of squares. Some people refer to n4 as n tesseracted, hypercubed, zenzizenzic, biquadrate or supercubed instead of "to the power of 4"
Fourth_power
1994 book by Michio Kaku
Dimension Cover depicting the artist's 2D conception of a 3D face of a 4D Hypercube house upon a 3D landscape Author Michio Kaku Language English Genre Popular
Hyperspace_(book)
In combinatorics
alphabet describes the vertices of an n {\displaystyle n} -dimensional hypercube, every two of which form a combinatorial line. The set of all combinatorial
Graham–Rothschild_theorem
Convex polyhedron projected from hypercube
in three-dimensional space, or as a three-dimensional projection of a hypercube. Zonohedra were originally defined and studied by E. S. Fedorov, a Russian
Zonohedron
Line segment in a circle or sphere from its center to its perimeter or surface
of the corresponding regular polygons. The radius of a d-dimensional hypercube with side s is r = s 2 d {\displaystyle r={\frac {s}{2}}{\sqrt {d}}} The
Radius
Discrete model of computation
considered to sit on the vertices of the 8-dimensional unit hypercube. This unit hypercube is the cellular automaton rule space. For next-nearest-neighbor
Cellular_automaton
Cube that fits through hole in smaller cube
n} -dimensional hypercube also has the Rupert property. Moreover, one may ask for the largest m {\displaystyle m} -dimensional hypercube that may be drawn
Prince_Rupert's_cube
Difficulties arising when analyzing data with many aspects ("dimensions")
10−n the 10-dimensional hypercube appears to be a factor of 10n(10−1) = [(10n)10/(10n)] "larger" than the 1-dimensional hypercube, which is the unit interval
Curse_of_dimensionality
Generalized sphere of dimension n (mathematics)
Fractal Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid
N-sphere
Group of symmetries of an n-dimensional hypercube
the square, the cube, and their higher-dimensional counterparts (the hypercubes), as well as the corresponding dual polytopes (the regular octahedron
Hyperoctahedral_group
1989 studio album by Voivod
4. "Missing Sequences" 5:49 5. "X-Ray Mirror" 4:28 6. "Inner Combustion" 3:48 7. "Pre-Ignition" 5:11 8. "Into My Hypercube" 5:03 9. "Sub-Effect" 4:29
Nothingface_(Voivod_album)
2021 studio album by Eyehategod
Joey LaCaze's death. The album was recorded at HighTower Records and Hypercube Studios, with producers Sanford Parker and James Whitten. On November
A_History_of_Nomadic_Behavior
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