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In mathematics, a cubical complex (also called cubical set and Cartesian complex) is a set composed of points, line segments, squares, cubes, and their
Cubical_complex
Abstract simplicial complex describing a graph's cliques
showed that a cubical complex (that is, a family of hypercubes intersecting face-to-face) forms a CAT(0) space if and only if the complex is simply connected
Clique_complex
Discrete (i.e., incremental) version of infinitesimal calculus
a chain complex. Another equivalent statement is that B k {\displaystyle B_{k}} is contained in Z k {\displaystyle Z_{k}} . A cubical complex is a set
Discrete_calculus
Formal linear combination in a cell complex
linear combination of the k-cells in a cell complex. In simplicial complexes (respectively, cubical complexes), k-chains are combinations of k-simplices
Chain_(algebraic_topology)
Type of topological space
R. (2011). Nonabelian Algebraic Topology:filtered spaces, crossed complexes, cubical homotopy groupoids. European Mathematical Society Tracts in Mathematics
CW_complex
Trapezohedron with eight faces
Alexander; Ziegler, Günter M. (2004), "Construction techniques for cubical complexes, odd cubical 4-polytopes, and prescribed dual manifolds", Experimental Mathematics
Tetragonal_trapezohedron
Three groups
shown that F acts as deck transformations on a locally finite CAT(0) cubical complex (necessarily of infinite dimension). A consequence is that F satisfies
Thompson_groups
Quotient of a weakly contractible space by a free action
) {\displaystyle \pi _{1}(M)} . A finite locally connected CAT(0) cubical complex is a classifying space of its fundamental group. The infinite-dimensional
Classifying_space
Method for computing topological features of a space at different spatial resolutions
the bringing of the filtered complex to its canonical form by upper-triangular matrices and runs in worst-case cubical complexity in the number of simplices
Persistent_homology
Four-dimensional analogue of the cube
six square faces, the hypersurface of the tesseract consists of eight cubical cells, meeting at right angles. The tesseract is one of the six convex
Tesseract
image at right. Mathematics portal Simplicial complex Cubical complex Reinhard Klette: Cell complexes through time. http://spie.org/Publications/Proceedings/Paper/10
Abstract_cell_complex
p} in these balls is convex. Cotangent bundle Covariant derivative Cubical complex Cut locus Diameter of a metric space is the supremum of distances between
Glossary of Riemannian and metric geometry
Glossary_of_Riemannian_and_metric_geometry
Family of infinite discrete groups
S'{}^{2}\rangle } is of spherical type. Such groups act cocompactly on a CAT(0) cubical complex, and, as a consequence, one can find a rational normal form for their
Artin–Tits_group
Concept in mathematics
{Conf} _{n}(\Gamma )} deformation retract to non-positively curved cubical complexes of dimension at most min ( n , b ( Γ ) ) {\displaystyle \min(n,b(\Gamma
Configuration space (mathematics)
Configuration_space_(mathematics)
discontinuously and cocompactly on a geodetically complete CAT(0) cubical complex X, then either X splits as a direct product of two unbounded convex
Acylindrically hyperbolic group
Acylindrically_hyperbolic_group
Conjecture linking two mathematical areas
acting properly on simply connected C A T ( 0 ) {\displaystyle CAT(0)} cubical complexes. Groups that admit a finite presentation with only one relation. Discrete
Baum–Connes_conjecture
Swiss-Indian mathematician
University of Côte d'Azur. Her research involves low-dimensional geometry, cubical complexes, and geometric group theory. She has also studied sexism and institutional
Indira_Chatterji
Analysis of datasets using techniques from topology
(gigabyte-scale) grayscale image data in dimension 1, 2 or 3 using cubical complexes and discrete Morse theory. Another R package, TDAstats, uses the Ripser
Topological_data_analysis
"Improved approximate rips filtrations with shifted integer lattices and cubical complexes". Journal of Applied and Computational Topology. 5 (3): 425–458. doi:10
Vietoris–Rips_filtration
-trees Coxeter groups Amenable groups Groups acting properly on CAT(0) cubical complexes Cherix, Pierre-Alain; Cowling, Michael; Jolissaint, Paul; Julg, Pierre;
Haagerup_property
Mathematical ranking of a set
Interdisciplinary Applied Mathematics, Springer, Section 9.4, Weak Orders and Cubical Complexes, pp. 188–196. Ziegler, Günter M. (1995), Lectures on Polytopes, Graduate
Weak_ordering
Large former industrial site in the city of Essen, North Rhine-Westphalia, Germany
gained notice for its simple, functional Bauhaus design with its mainly cubical buildings made of reinforced concrete and steel trusses. The shaft's characteristic
Zollverein Coal Mine Industrial Complex
Zollverein_Coal_Mine_Industrial_Complex
Area in mathematics devoted to the study of finitely generated groups
applications. The study of group actions on CAT(0) spaces and CAT(0) cubical complexes, motivated by ideas from Alexandrov geometry. Interactions with low-dimensional
Geometric_group_theory
Plastic building toy brand
Construx feature beam-like pieces of varying lengths that snapped on to cubical connector knots in order to build large shapes. These are relatively secure
Construx
Species of fungus
sulphureus is a saprophyte and occasionally a weak parasite, causing brown cubical rot in the heartwood of trees on which it grows. Unlike many bracket fungi
Laetiporus_sulphureus
Croatian-American mathematician
Bestvina and Brady developed a version of discrete Morse theory for cubical complexes and applied it to study homological finiteness properties of subgroups
Mladen_Bestvina
Polynomial equation of degree 3
rational coefficients have roots that are irrational (and even non-real) complex numbers. Cubic equations were known to the ancient Babylonians, Greeks
Cubic_equation
Tissue lining the surfaces of organs in animals
are 5 main types of cell junctions, each composed of different protein complexes: Tight junctions are a formed by pairs of trans-membrane proteins that
Epithelium
Equivalence between the categories of chain complexes and simplicial abelian groups
Rafael (2011). Nonabelian Algebraic Topology: filtered spaces, crossed complexes, cubical homotopy groupoids. Tracts in Mathematics. Vol. 15. Zurich: European
Dold–Kan_correspondence
American mathematician
group is a key object in the version of discrete Morse theory for cubical complexes developed by Mladen Bestvina and Noel Brady and in the study of subgroups
John_R._Stallings
Historic site in Karnataka, India
large cubical sukanasa containing a Surya (Sun god) icon. Much of the Badigargudi relief artwork has been damaged and eroded. The Durga temple complex houses
Aihole
Number whose cube is a given number
x_{n+1}=x_{n}\left({\frac {x_{n}^{3}+2a}{2x_{n}^{3}+a}}\right).} This converges cubically, so two iterations do as much work as three iterations of Newton's method
Cube_root
Ancient and medieval monuments, a UNESCO World Heritage Site in Karnataka, India
Vishnu in Hampi. The 3 metres (9.8 ft) Shiva Linga stands in water in a cubical chamber and has three eyes sketched on its top. South of this is the shrine
Hampi
Branch of mathematics
3-Manifolds, Right-Angled Artin Groups, and Cubical Geometry: 3-manifolds, Right-angled Artin Groups, and Cubical Geometry. American Mathematical Soc.
Geometry
Branch of mathematics
Rafael (2011), Nonabelian Algebraic Topology: Filtered Spaces, Crossed Complexes, Cubical Homotopy Groupoids, European Mathematical Society Tracts in Mathematics
Algebraic_topology
Graph whose maximal clique hypergraph is a hypertree
the intersection graphs of maximal hypercubes of graphs of acyclic cubical complexes. The structure and algorithmic use of doubly chordal graphs is given
Dually_chordal_graph
Subdivision of space into cells
simplicial complex is a mesh composed of simplices. Most polyhedral (e.g. cubical) meshes are conformal, meaning they have the cell structure of a CW complex, a
Mesh_generation
Four-dimensional analog of the octahedron
The cell-first parallel projection of the 16-cell into 3-space has a cubical envelope. The closest and farthest cells are projected to inscribed tetrahedra
16-cell
Mathematical foam of equal-volume bubbles
prisms called tetrastix. These prisms surround cubical voids which form one fourth of the cells of the cubical tiling; the remaining three fourths of the
Weaire–Phelan_structure
United States historic place
connected via a wooden ell to the 1903 jail. That building was a basically cubical masonry structure, two stories in height, finished in brick with granite
Orleans County Courthouse and Jail Complex
Orleans_County_Courthouse_and_Jail_Complex
Buddhist temple in Kathmandu, Nepal
looking in all four directions. The gold plated bronze rings above the cubical structure are called Trayodashabhuvana (thirteen steps) representing the
Swayambhunath
Concept in algebraic topology
approximations" (PDF). Topology Proceedings. 24: 503–532. Topological methods in scientific computing Computational homology (also cubical homology)
Simplicial_homology
UNESCO World Heritage Site in Isfahan, Iran
years. First Stage: The initial building acting as entrance to the complex was in cubical shape and in two stories, with dimensions measuring 20 x 19 meter
Ali_Qapu
Species of lichen
with P. atropurpurea, which has smaller fruiting bodies and rounded, not cubical, spore lumina; he also discussed similarities and differences with P. circumfiniens
Pyrenula_cubica
Generalization of category theory
Rafael (2011). Nonabelian algebraic topology: filtered spaces, crossed complexes, cubical homotopy groupoids. Tracts in Mathematics. Vol. 15. European Mathematical
Higher_category_theory
Any species of fungus that digests moist wood, causing it to rot
shows a brown discoloration, and cracks into roughly cubical pieces, a phenomenon termed cubical fracture. The fungi of certain types remove cellulose
Wood-decay_fungus
Swiss chemist (1866–1919)
later in 1916 when Gilbert N. Lewis formulated the "octet rule" in his cubical atom theory. In modern terminology, Werner's primary valence corresponds
Alfred_Werner
Algebraic construct classifying topological spaces
Rafael Sivera, Nonabelian algebraic topology: filtered spaces, crossed complexes, cubical homotopy groupoids, EMS Tracts in Mathematics Vol. 15, 703 pages,
Homotopy_group
Catholic basilica in Rome
architectural spaces, developed from a Greek cross, with a dominant transept, with cubical chapels at each end, and the effect of a transverse nave. There is no true
Santa Maria degli Angeli e dei Martiri
Santa_Maria_degli_Angeli_e_dei_Martiri
Atomic model introduced by Niels Bohr in 1913
Joseph Larmor's Solar System model (1897), Jean Perrin's model (1901), the cubical model (1902), Hantaro Nagaoka's Saturnian model (1904), the plum pudding
Bohr_model
Mathematical theorem
(2011), Nonabelian algebraic topology: filtered spaces, crossed complexes, cubical homotopy groupoids, European Mathematical Society Tracts in Mathematics
Eckmann–Hilton_argument
Type theory in logic and mathematics
computational behavior of the univalence axiom in homotopy type theory. Cubical type theory is one attempt to give computational content to homotopy type
Homotopy_type_theory
Mathematical theory of data types
intuitionistic type theory mostly by its handling of the equality type. In 2016, cubical type theory was proposed, which is a homotopy type theory with normalization
Type_theory
Species of fungus
of Fomes are usually taller than wide. The perennial woody conk causes cubical brown rot typical of Fomitopsis. It favours aspen or conifer trees. It
Fomitopsis_mounceae
Area for keeping and raising animals or plants
enclosures and are able to withstand high degrees of humidity. They may be cubical, spherical, cuboidal, or other shapes. The choice of materials depends
Vivarium
City in Uttar Pradesh, India
found and the complex itself appeared to be a pottery workshop. Ceramic items found included roof tiles, dishes, cups, vases, cubical dice, beads, terracotta
Bijnor
Convex polytope, the n-dimensional analogue of a square and a cube
Edition. New York: John Wiley & Sons. ISBN 0-471-39882-9. Cf Chapter 7.1 "Cubical Representation of Boolean Functions" wherein the notion of "hypercube"
Hypercube
Fictional faction in Star Trek
spacefaring "mites" (the whale-probe's term for humanoid races) who traveled in cubical and spherical spacefaring vessels; the Borg apparently attacked the whale-probe
Borg
Ministry of Defence R&D agency in India
enclosure of intubation procedure made with Poly(methyl methacrylate). It is cubical designed for both adults and minors and covers the COVID-19-infected patients
Defence Research and Development Organisation
Defence_Research_and_Development_Organisation
Bronze Age civilisation in South Asia
mostly toys. The Harappans also made various toys and games, among them cubical dice (with one to six holes on the faces), which were found in sites like
Indus_Valley_Civilisation
Shape made from cubes joined together
of the chiral tetracube. Polycubes are classified according to how many cubical cells they have: Fixed polycubes (both reflections and rotations counted
Polycube
Describes the fundamental group in terms of a cover by two open path-connected subspaces
Rafael Sivera. Nonabelian Algebraic Topology: filtered spaces, crossed complexes, cubical homotopy groupoids, European Mathematical Society Tracts vol 15, August
Seifert–Van_Kampen_theorem
Function describing an electron in an atom
The orbitals with a well-defined magnetic quantum number are generally complex-valued. Real-valued orbitals can be formed as linear combinations of mℓ
Atomic_orbital
Concept in category theory
(2011). Nonabelian Algebraic Topology: filtered spaces, crossed complexes, cubical omega-groupoids. Tracts in Mathematics. Vol. 15. European Mathematical
Fibred_category
Iranian tomb complex erected in honor of the Persian poet Ferdowsi
Taherzadeh, who replaced the old dome-shaped design by Lurzadeh with a modern cubical design. Ferdowsi's tomb, which resembles the tomb of Cyrus the Great, is
Tomb_of_Ferdowsi
Chemical rule of thumb
referred to this insight as Abegg's rule and used it to help formulate his cubical atom model and the "rule of eight", which began to distinguish between
Octet_rule
Seminal math text
globular groupoids, and observed there should be a corresponding theory using cubical sets, he came up with the idea of test categories and test functors.pg
Pursuing_Stacks
Medical college in Lahore, Pakistan
On average, there are 112 rooms in each hostel with rooms ranging from cubical, twin, and four-bed. The hostel facilities can accommodate 1,000 students
Allama_Iqbal_Medical_College
Stem decay fungus
with the advanced stage appearing as a brown and crumbly breaking into cubical pieces. Wood impacted by this fungus may become more brittle and prone
Fomitopsis_pinicola
Polyhedron with 8 triangles and 6 squares
The graph of a cuboctahedron may be constructed as the line graph of the cubical graph, making it becomes the locally linear graph. The 24 edges can be
Cuboctahedron
Nuclear reactor design
interior of the primary containment and the outer shield wall, and is cubical in shape. One major enhancement is that the reactor has a standard safe
Advanced boiling water reactor
Advanced_boiling_water_reactor
Bosnian-American mathematician
Electoral Maps, and Representation, Princeton University Press, 2024. 408 pp. Cubical homotopy theory, with B. Munson, New Mathematical Monographs, 25. Cambridge
Ismar_Volić
Combining capacity of elements with other atoms
valence led to the modern theories of chemical bonding, including the cubical atom (1902), Lewis structures (1916), valence bond theory (1927), molecular
Valence_(chemistry)
Archaeological site in Punjab, Pakistan
of present-day Pakistan. There is evidence that citizens stopped using cubical weights, square steatite seals and statues of the mother goddess during
Ganweriwal
Structures at San Lorenzo, Florence, Italy
Lorenzo, with which it consciously competes, and shares its format of a cubical space surmounted by a dome, of gray pietra serena and whitewashed walls
Medici_Chapels
Algorithms for calculating square roots
method, which is the Householder's method of order two. This converges cubically, but involves five multiplications per iteration: y n = S ⋅ x n 2 , {\displaystyle
Square_root_algorithms
period ranging from the various dice games to other board games. The use of cubical and oblong dice was common in the Indus Valley Harappan civilization (c
History_of_games
Ancient Egyptian official, priest
they did not inherit their father's condition. The sculpture's roughly cubical arrangement cleverly ensures that the overall composition retains a harmonious
Seneb
Historical architecture style
Zoroastrian icon, Faravahar. One of the enigmatic features of the complex is a cubical, stone structure standing 12.5 meters tall, and around 7 meters wide
Achaemenid_architecture
Mathematical technique
interact only with adjacent subsystems. For example, a three-dimensional cubical lattice of spins in an Ising model can be decomposed into a sequence of
Transfer-matrix method (statistical mechanics)
Transfer-matrix_method_(statistical_mechanics)
Historic house in Connecticut, United States
type popular with wealthy Victorians embracing the Picturesque mode: a cubical form, nearly flat roof with wide overhanging eaves, and a three-bay facade
John_Kendrick_House
Atomic model
spherical harmonics are complex functions. The complex numbers are two-dimensional with a real part and an imaginary part. Complex numbers offer very handsome
Cubic_harmonic
Greek island in the Aegean Sea
of Santorini is similar to that of the other Cyclades, with low-lying cubical houses, made of local stone and whitewashed or limewashed with various
Santorini
Mausoleum (Uzbek: Arabota maqbarasi, lit. 'Shrine of the Arab Father') is a cubical, domed brick mausoleum built in 977-78 in the village of Tim, Samarqand
Arab-Ata_Mausoleum
Mosque in Damascus, Syria
the top of the main tower, before the roof, with horseshoe arches and cubical capitals enclosed in a single arch. A smaller arched corbel is located
Umayyad_Mosque
Type of wind tunnel
tunnel increases linearly with its cross section and flow density, but cubically with the test velocity required. Hence installation of a continuous, closed
Hypersonic_wind_tunnel
Four-dimensional analogues of the regular polyhedra in three dimensions
256–. ISBN 978-0-691-15457-2. Coxeter 1973, § 1.8 Configurations Coxeter, Complex Regular Polytopes, p. 117 Conway, Burgiel & Goodman-Strauss 2008, p. 406
Regular_4-polytope
Set of principles for modeling solid geometry
schemes are a particular case of cell decompositions where all the cells are cubical and lie in a regular grid. Cell decompositions provide convenient ways
Solid_modeling
10th-century Hindu temple in Bhubaneshwar, Odisha, India
exhibiting feminine charms entwined with nagas and naginis. The sanctum is cubical from the inside with offset walls on the outside. This distinctive 10th-century
Mukteshvara Temple, Bhubaneswar
Mukteshvara_Temple,_Bhubaneswar
Notion of equality in type theory
branches of research into the identity type are homotopy type theory and its cubical type theory. "Identity Type". nLab. Retrieved 19 January 2022. Martin-Löf
Identity_type
Electromechanical fire control computer
The Ford Mark 1/1A mechanism was mounted into a pair of approximately cubical large castings with very wide openings, the latter covered by gasketed
Rangekeeper
Device for controlled nuclear reactions
Molten-salt reactor Molten metal reactor (e.g. LAMPRE) Gas fueled (theoretical) Cubical Cylindrical Octagonal Spherical Slab Annulus Electricity Nuclear power
Nuclear_reactor
Polytope with highest degree of symmetry
remaining 6 cubical faces of the tesseract. The 24-cell can be derived from the tesseract by joining the 8 vertices of each of its cubical faces to an
Regular_polytope
Flat-sided three-dimensional shape
original work is lost and his solids come down to us through Pappus. Both cubical dice and 14-sided dice in the shape of a truncated octahedron in China
Polyhedron
Self-contained cartridge loaded with either shot or a solid slug
solutions. Intentionally deformed shot (hammered into ellipsoidal shape) or cubical shot will also result in a wider pattern, much wider than spherical shot
Shotgun_cartridge
U.S. national memorial in Washington, D.C.
monument, has a marble capstone shaped like a truncated pyramid, with a cubical keystone projecting from its base and a deep groove surrounding the keystone
Washington_Monument
Prominent city of the ancient Indus valley civilization (present-day Gujarat, India)
The remnants of the north–south sewer are burnt bricks in the cesspool. Cubical blocks of the warehouse on a high platform are also visible. The ASI has
Lothal
Village in Tamil Nadu, India
staircases in front of each, consisting of three steps. The cells are all cubical and empty, with no dvarpalas or inscriptions. This shrine would have had
Mamandur
Species of conifer
undulata, and Postia sericeomollis. P. sericeomollis is responsible for brown cubical butt and pocket rot of cedar. It is the second-most common cause of decay
Thuja_plicata
Open question in philosophy of how abstract minds interact with physical bodies
body as uncomplicated, in the same way that it is uncomplicated that a cubical shape is a property of a toy building block. The soul is a property exhibited
Mind–body_problem
CUBICAL COMPLEX
CUBICAL COMPLEX
Girl/Female
Tamil
Nanduni | நாநà¯à®¤à¯à®¨à¯€
Musical instrument
Nanduni | நாநà¯à®¤à¯à®¨à¯€
Boy/Male
Tamil
Musical
Girl/Female
Tamil
Musical instrument
Girl/Female
Indian, Telugu
Musical
Boy/Male
Assamese, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Tamil, Telugu
Musical
Male
Celtic
, sportive.
Girl/Female
Tamil
Musical instrument
Girl/Female
Tamil
Musical instrument
Boy/Male
Hindu, Indian
Musical
Boy/Male
Tamil
Musical
Girl/Female
Tamil
Musical instrument
Girl/Female
Tamil
Musical Rhythm
Boy/Male
Tamil
Musical instrument
Boy/Male
Hindu, Indian
Musical
Boy/Male
Indian, Sikh
Musical
Girl/Female
Indian, Tamil
Musical
Boy/Male
Hindu
Musical
Biblical
musical
Girl/Female
Tamil
Musical notes
Boy/Male
Tamil
Musical notes
CUBICAL COMPLEX
CUBICAL COMPLEX
Girl/Female
Indian, Punjabi, Sikh
Shape
Girl/Female
Tamil
River Yamuna, Born of the Sun
Girl/Female
Muslim
A plant that grows in quick
Female
Hungarian
Pet form of Hungarian Erzsébet, ZSÓKA means "God is my oath."
Boy/Male
British, English
From the Ridge Meadow
Biblical
judgment; covering; habit
Boy/Male
British, French, Hindu, Indian, Tamil
Nice Person
Boy/Male
Australian, German, Greek, Italian
Order; From Cosmos; Beauty
Boy/Male
Hindu, Indian, Punjabi, Sikh
Soldier
Girl/Female
Tamil
Elampirai | இலாமபிராஈ
Young crescent
CUBICAL COMPLEX
CUBICAL COMPLEX
CUBICAL COMPLEX
CUBICAL COMPLEX
CUBICAL COMPLEX
a.
Plane or flat on one side, and conical on the other.
a.
Colored a prevailing red, bay, or black, with flecks of white or gray especially on the flanks; -- said of horses.
a.
Of or pertaining to music; having the qualities of music; or the power of producing music; devoted to music; melodious; harmonious; as, musical proportion; a musical voice; musical instruments; a musical sentence; musical persons.
a.
Isometric or monometric; as, cubic cleavage. See Crystallization.
a.
Of or pertaining to the rubric or rubrics.
a.
Having the form or properties of a cube; contained, or capable of being contained, in a cube.
n.
The quality of being cubical.
n.
A sleeve covering the arm from the elbow to the hand.
a.
Exciting mirth; droll; laughable; as, a comical story.
a.
Given to sneering at rectitude and the conduct of life by moral principles; disbelieving in the reality of any human purposes which are not suggested or directed by self-interest or self-indulgence; as, a cynical man who scoffs at pretensions of integrity; characterized by such opinions; as, cynical views of human nature.
a.
Of the length of a cubit.
a.
Having the form of, or resembling, a geometrical cone; round and tapering to a point, or gradually lessening in circumference; as, a conic or conical figure; a conical vessel.
n.
Any small cubical or square body.
a.
Having a mixture of seriousness and sport; serious and comical.
a.
Colored in, or marked with, red; placed in rubrics.
n.
A social entertainment of which music is the leading feature; a musical party.
a.
Of or pertaining to the cubit or ulna; as, the cubital nerve; the cubital artery; the cubital muscle.
a.
Alt. of Cubical
n.
A cubical vessel containing a Roman cubic foot, each side being a Roman square foot; -- used as a measure.
adv.
In a cubical method.