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Concept in algebraic geometry
In algebraic geometry, a toroidal embedding is an open embedding of algebraic varieties that locally looks like the embedding of the open torus into a
Toroidal_embedding
Partition of a toroidal surface into polygons
"Toroidal polyhedron". MathWorld. Stewart Toroids (Toroidal Solids with Regular Polygon Faces) Stewart's polyhedra Toroidal Polyhedra Stewart toroids
Toroidal_polyhedron
Embedding a graph in a topological space, often Euclidean
embedding, cellular embedding or map is an embedding in which every face is homeomorphic to an open disk. A closed 2-cell embedding is an embedding in
Graph_embedding
Doughnut-shaped surface of revolution
of the polyhedron. The term "toroidal polyhedron" is also used for higher-genus polyhedra and for immersions of toroidal polyhedra, although some authors
Torus
Algebraic variety containing an algebraic torus
replacing the step of taking a GIT quotient by a quotient stack) Toroidal embedding Cox, David (2003), "What is a toric variety?" (PDF), Topics in algebraic
Toric_variety
Graph able to be embedded on a torus
be embedded in a plane can also be embedded in a torus, so every planar graph is also a toroidal graph. A toroidal graph that cannot be embedded in a
Toroidal_graph
48 edges, and 16 hexagonal cycles. It is the dual of its symmetric toroidal embedding is the Shrikhande graph. It can be visualized as net, a 4 by 4 array
Dyck_graph
American mathematician (born 1937)
varieties appeared in 1966–7. He also is one of the founders of the toroidal embedding theory, the geometric approach to varieties defined by monomials.
David_Mumford
Symmetric tessellation of a closed surface
generally regular toroidal polyhedra {p,q}b,c can be defined if either p or q are even, although only euclidean ones above can exist as toroidal polyhedra in
Regular_map_(graph_theory)
3-dimensional object
product topology. A standard way to visualize a solid torus is as a toroid, embedded in 3-space. However, it should be distinguished from a torus, a surface
Solid_torus
Branch of mathematics that studies the properties of groups
direction, toric varieties are algebraic varieties acted on by a torus. Toroidal embeddings have recently led to advances in algebraic geometry, in particular
Group_theory
Toroidal polyhedron with 7 faces
the seven colour theorem. The other half of the theorem states that all toroidal subdivisions can be colored with seven or fewer colors. The Szilassi polyhedron
Szilassi_polyhedron
Class of compact connected topological spaces
place of the circle, together with an expanding self-immersion. In the toroidal coordinates with radius R {\displaystyle R} , the solenoid can be parametrized
Solenoid_(mathematics)
Graph that can be embedded in the plane
planar graph. A 1-outerplanar embedding of a graph is the same as an outerplanar embedding. For k > 1 a planar embedding is k-outerplanar if removing the
Planar_graph
Mathematical concept
{\bar {X}}} is proper. Tropical geometry GIT quotient Chow quotient Toroidal embedding Tevelev, Jenia (2007-08-07). "Compactifications of subvarieties of
Tropical_compactification
Branch of the mathematical field of graph theory
the embedding of graphs in surfaces, spatial embeddings of graphs, and graphs as topological spaces. It also studies immersions of graphs. Embedding a graph
Topological_graph_theory
Toroidal polyhedron with 14 triangle faces
geometry, the Császár polyhedron (Hungarian: [ˈt͡ʃaːsaːr]) is a nonconvex toroidal polyhedron with 14 triangular faces. This polyhedron has no diagonals;
Császár_polyhedron
Ideas from Mathematics have been used as inspiration for fiber arts
Knitted and crocheted tori have also been constructed depicting toroidal embeddings of the complete graph K7 and of the Heawood graph. The crocheting
Mathematics_and_fiber_arts
Retrieved 25 August 2017. Ambro, Florin (2013). "Cyclic covers and toroidal embeddings". arXiv:1310.3951 [math.AG]. Fedorchuk, Maksym (2011-05-13). "Cyclic
Cyclic_cover
Mathematical theory in the field of algebraic geometry
G.; Knudsen, Finn Faye; Mumford, David; Saint-Donat, B. (1973), Toroidal Embeddings I, Lecture Notes in Mathematics, vol. 339, Berlin, New York: Springer-Verlag
Semistable_reduction_theorem
Cycles in a graph that cover each edge twice
an embedding on a manifold: the cell complex formed by the cycles of the cover may have non-manifold topology at its vertices. The circular embedding conjecture
Cycle_double_cover
Geometric algorithm
the corresponding eigenvectors. Step 5. Use diffusion map to get the embedding Ψ t {\displaystyle \Psi _{t}} . In the paper Nadler et al. showed how
Diffusion_map
Graph representing faces of another graph
graph K7 is a toroidal graph: it is not planar but can be embedded in a torus, with each face of the embedding being a triangle. This embedding has the Heawood
Dual_graph
Symmetric bipartite cubic graph with 16 vertices and 24 edges
topological embedding of the Möbius–Kantor graph cannot be realized as a non-self-crossing toroidal polyhedron. The dual graph of this embedding is the hyperoctahedral
Möbius–Kantor_graph
Undirected graph named after S. S. Shrikhande
is a toroidal graph. The embedding forms a regular map in the torus, with 32 triangular faces. The skeleton of the dual of this map (as embedded in the
Shrikhande_graph
Mathematical object studied in the field of algebraic geometry
Segre embedding. Furthermore, any variety that admits one embedding into projective space admits many others, for example by composing the embedding with
Algebraic_variety
Theorem on graph coloring on surfaces
forms an embedding of the Heawood graph onto the torus. Grünbaum, Branko; Szilassi, Lajos (2009), "Geometric Realizations of Special Toroidal Complexes"
Heawood_conjecture
Undirected graph with 14 vertices
6-cycles, is the Coxeter graph. The Heawood graph is a toroidal graph; that is, it can be embedded without crossings onto a torus. The result is the regular
Heawood_graph
American research organization
The Center for Embedded Networked Sensing (CENS) was a research enterprise funded by the National Science Foundation based at the University of California
Center for Embedded Network Sensing
Center_for_Embedded_Network_Sensing
Mathematical puzzle of avoiding crossings
K_{3,3}} is a toroidal graph, which means that it can be embedded without crossings on a torus, a surface of genus one. These embeddings solve versions
Three_utilities_problem
24-vertex symmetric bipartite cubic graph
The dual graph of this embedding is a symmetric 6-regular graph with 12 vertices and 36 edges. The other symmetric embedding of the Nauru graph has six
Nauru_graph
Electricity generation by nuclear fusion
magnetic field. A spheromak has both toroidal and poloidal fields, while a field-reversed configuration has no toroidal field. Dynomak: A spheromak that is
Fusion_power
Experimental physics device
The Enormous Toroidal Plasma Device (ETPD) is an experimental physics device housed at the Basic Plasma Science Facility at University of California, Los
Enormous Toroidal Plasma Device
Enormous_Toroidal_Plasma_Device
Cycle graph with all opposite nodes linked
and can be embedded without crossings on a torus or projective plane. Thus, they are examples of toroidal graphs. Li (2005) explores embeddings of these
Möbius_ladder
Finiteness of sets of forbidden graph minors
set of toroidal graphs has a finite obstruction set, but it does not provide any such set. The complete set of forbidden minors for toroidal graphs remains
Robertson–Seymour_theorem
Collection of ideas in music theory
Planet-4D model, a new visualisation system based on graph theory that embeds the traditional Tonnetz on a 4D Hypersphere. Another recent continuous version
Neo-Riemannian_theory
Non-orientable mathematical surface
strip is a subset of a solid torus, the Möbius tube is a subset of a toroidally closed spherinder (solid spheritorus). The following parametrization of
Klein_bottle
Bipartite, 3-regular undirected graph
second, to form a regular map with 18 triangular faces. The two regular toroidal maps are dual to each other. The automorphism group of the Pappus graph
Pappus_graph
Fictional universe created by Iain M. Banks
atmosphere created by Larry Niven in The Integral Trees, but spherical not toroidal, require a force field to retain their integrity, and arose by artificial
The_Culture
April 2023. Namikawa, Yukihiko (1980). "Main problem and main results". Toroidal Compactification of Siegel Spaces. Lecture Notes in Mathematics. Vol. 812
List of letters used in mathematics, science, and engineering
List_of_letters_used_in_mathematics,_science,_and_engineering
Number of "holes" of a surface
polygon. Genus of orientable surfaces Planar graph: genus 0 Toroidal graph: genus 1 Double Toroidal graph: genus 2 Pretzel graph: genus 3 The non-orientable
Genus_(mathematics)
Ability of cell membranes to deform elastically
1103/physreva.41.4517, PMID 9903652 Mutz, M.; Bensimon, D. (1991), "Observation of toroidal vesicles", Physical Review A, 43 (8): 4525–4527, Bibcode:1991PhRvA..43
Elasticity_of_cell_membranes
Hospital in Los Angeles, California
Film and Television Centers NanoSystems Embedded Network Sensing Study of Women Chicano Studies Enormous Toroidal Plasma Device Film and Television Archive
Ronald Reagan UCLA Medical Center
Ronald_Reagan_UCLA_Medical_Center
Star at the centre of the Solar System
internal toroidal magnetic field to the external poloidal field, and sunspots diminish in number and size. At solar-cycle minimum, the toroidal field is
Sun
is a graph that has such an embedding onto the Euclidean plane, and a toroidal graph is a graph that has such an embedding onto a torus. The genus of a
Glossary_of_graph_theory
Method of describing higher-order polyhedra
Floret pentagonal tiling gΔ = gH Conway operators can also be applied to toroidal polyhedra and polyhedra with multiple holes. A 1x1 regular square torus
Conway_polyhedron_notation
trigonometric forms) Oblate spheroidal chart (rational and trigonometric forms) Toroidal chart Hyperbolic spaces n-dimensional hyperbolic space Hn Upper half-space
List_of_coordinate_charts
Surface containing a line through every point
are also sometimes considered as abstract algebraic surfaces without an embedding into affine or projective space, in which case "straight line" is understood
Ruled_surface
Film and Television Centers NanoSystems Embedded Network Sensing Study of Women Chicano Studies Enormous Toroidal Plasma Device Film and Television Archive
List of UCLA Anderson School of Management people
List_of_UCLA_Anderson_School_of_Management_people
Flat-sided three-dimensional shape
Timaeus, later soon treatment studied in Euclid's Elements. In Renaissance, toroidal polyhedra were used for sketching on polyhedral's perspective views, skeletal
Polyhedron
4-dimensional object
between. the duocylinder (2-ball × 2-ball), whose surface consists of two toroidal cells. The duocylinder is the only one of the above three that is regular
Duocylinder
Cubic graph with 8 vertices and 12 edges
making it an apex graph. It can be embedded without crossings on a torus or projective plane, so it is also a toroidal graph. It has girth 4, diameter 2
Wagner_graph
displayed to the public at the Canadian National Exhibition. 1950: The Toroidal chamber with axial magnetic fields (the Tokamak) is developed by Igor E
Timeline of historic inventions
Timeline_of_historic_inventions
Concept in algebraic geometry
resolve the singularities of a variety X embedded into a larger variety W. Suppose we have a closed embedding of X into a regular variety W. A strong desingularization
Resolution_of_singularities
Mathematical object
another choice of hyperspherical coordinates, (η, ξ1, ξ2), makes use of the embedding of S3 in C2. In complex coordinates (z1, z2) ∈ C2 we write z 1 = e i ξ
3-sphere
projective-plane embeddings of graphs with planar covers The strong Papadimitriou–Ratajczak conjecture: every polyhedral graph has a convex greedy embedding Turán's
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
2024 occupation protest in Los Angeles, California
Film and Television Centers NanoSystems Embedded Network Sensing Study of Women Chicano Studies Enormous Toroidal Plasma Device Film and Television Archive
2024 University of California, Los Angeles pro-Palestinian campus occupation
2024_University_of_California,_Los_Angeles_pro-Palestinian_campus_occupation
Public medical school in Los Angeles, California, US
Film and Television Centers NanoSystems Embedded Network Sensing Study of Women Chicano Studies Enormous Toroidal Plasma Device Film and Television Archive
David Geffen School of Medicine at UCLA
David_Geffen_School_of_Medicine_at_UCLA
Healthcare network in California, United States
Film and Television Centers NanoSystems Embedded Network Sensing Study of Women Chicano Studies Enormous Toroidal Plasma Device Film and Television Archive
UCLA_Health
Public continuing education institution
Film and Television Centers NanoSystems Embedded Network Sensing Study of Women Chicano Studies Enormous Toroidal Plasma Device Film and Television Archive
UCLA_Extension
certain Seifert manifolds. A 3-manifold that is not atoroidal is called toroidal. Apanasov, Boris N. (2000), Conformal Geometry of Discrete Groups and Manifolds
Atoroidal
School within the University of California, Los Angeles
Film and Television Centers NanoSystems Embedded Network Sensing Study of Women Chicano Studies Enormous Toroidal Plasma Device Film and Television Archive
UCLA School of Theater, Film and Television
UCLA_School_of_Theater,_Film_and_Television
Garden in Los Angeles, California, United States
Film and Television Centers NanoSystems Embedded Network Sensing Study of Women Chicano Studies Enormous Toroidal Plasma Device Film and Television Archive
Hannah_Carter_Japanese_Garden
of Levi graph for the edges and triangular faces of a certain locally toroidal abstract regular 4-polytope. It is therefore the first in an infinite family
Gray_graph
Device performing a Boolean function
other symbols in combination to form complex symbols (for example, use as embedded symbols) is discouraged." This compromise was reached between the respective
Logic_gate
Linguistic database
Film and Television Centers NanoSystems Embedded Network Sensing Study of Women Chicano Studies Enormous Toroidal Plasma Device Film and Television Archive
UCLA Phonological Segment Inventory Database
UCLA_Phonological_Segment_Inventory_Database
Public affairs school of UCLA
Film and Television Centers NanoSystems Embedded Network Sensing Study of Women Chicano Studies Enormous Toroidal Plasma Device Film and Television Archive
UCLA Luskin School of Public Affairs
UCLA_Luskin_School_of_Public_Affairs
Film and Television Centers NanoSystems Embedded Network Sensing Study of Women Chicano Studies Enormous Toroidal Plasma Device Film and Television Archive
UCLA Asian American Studies Center
UCLA_Asian_American_Studies_Center
Reaction that combines atomic nuclei
it are magnetic confinement (toroid designs) and inertial confinement (laser designs). Workable designs for a toroidal reactor that theoretically will
Nuclear_fusion
Library at UCLA
Film and Television Centers NanoSystems Embedded Network Sensing Study of Women Chicano Studies Enormous Toroidal Plasma Device Film and Television Archive
Powell_Library
Official mascot of UCLA
Film and Television Centers NanoSystems Embedded Network Sensing Study of Women Chicano Studies Enormous Toroidal Plasma Device Film and Television Archive
Joe_Bruin
Sports equipment for ice hockey
used on floors. Open disk hockey pucks have a hole, forming the shape of a toroid, for use in a particular style of floor hockey. They should not be confused
Hockey_puck
Type of weapon that fires a concentrated beam of energy at its target
requiring brief and extremely large amounts of energy) to accelerate a toroid of plasma at a significant percentage of the speed of light. The Russian
Directed-energy_weapon
Neighborhood of Los Angeles in California, United States
Film and Television Centers NanoSystems Embedded Network Sensing Study of Women Chicano Studies Enormous Toroidal Plasma Device Film and Television Archive
Westwood,_Los_Angeles
Method of storing energy
(PDF). U.S. Department of Energy. Retrieved 23 February 2026. Torotrak Toroidal variable drive CVT Archived May 16, 2011, at the Wayback Machine, retrieved
Flywheel_energy_storage
Three linked but pairwise separated rings
three-dimensional space by embedding the plane into space and deforming the curves drawn on it above or below the embedded plane at each crossing, as
Borromean_rings
Harald Schwarz invented a Go variant that is played on a circular lattice. Toroidal (or Torus Go) is played on a two-dimensional doughnut shaped surface. It
Go_variants
Reflection Nebula in Andromeda
embedded in the cloud. The cloud's magnetic field geometry, studied via polarimetric observations of background stars, shows a predominantly toroidal
VdB_158
Student hackathon at UCLA
Film and Television Centers NanoSystems Embedded Network Sensing Study of Women Chicano Studies Enormous Toroidal Plasma Device Film and Television Archive
LA_Hacks
Archive for film and television production
Film and Television Centers NanoSystems Embedded Network Sensing Study of Women Chicano Studies Enormous Toroidal Plasma Device Film and Television Archive
UCLA Film & Television Archive
UCLA_Film_&_Television_Archive
College of the University of California, Los Angeles
Film and Television Centers NanoSystems Embedded Network Sensing Study of Women Chicano Studies Enormous Toroidal Plasma Device Film and Television Archive
UCLA College of Letters and Science
UCLA_College_of_Letters_and_Science
Model of electrically conducting fluids
equation, derived from ideal MHD, describes the equilibrium of axisymmetric toroidal plasma in a tokamak. In tokamak experiments, the equilibrium during each
Magnetohydrodynamics
Tire that fits on the wheel of a bicycle
essentially toroidal thin-walled pressure vessels and if the carcass is treated as a homogeneous and isotropic material then stress in the toroidal direction
Bicycle_tire
American public research university
Film and Television Centers NanoSystems Embedded Network Sensing Study of Women Chicano Studies Enormous Toroidal Plasma Device Film and Television Archive
University of California, Los Angeles
University_of_California,_Los_Angeles
Trajectory of a beam of accelerated particles
Focusing mirrors - one or more mirrors, which may be flat, bent-flat, or toroidal, which helps to collimate (focus) the beam Monochromators - devices based
Beamline
Graphical method to simplify Boolean expressions
cells where A is true and D is false (that is, D is true). The grid is toroidally connected, which means that rectangular groups can wrap across the edges
Karnaugh_map
Construction assembly for absorbing thermally-induced volume changes
(pressure balanced expansion joints are a type of metal expansion joint), toroidal expansion joint, gimbal expansion joint, universal expansion joint, in-line
Expansion_joint
Research and policy think tank focused on racial justice
Film and Television Centers NanoSystems Embedded Network Sensing Study of Women Chicano Studies Enormous Toroidal Plasma Device Film and Television Archive
The Civil Rights Project/Proyecto Derechos Civiles
The_Civil_Rights_Project/Proyecto_Derechos_Civiles
British mathematician (1916–2020)
S2CID 120649715. Guy, R. K.; Jenkyns, Tom; Schaer, Jonathan (1968). "The toroidal crossing number of the complete graph". J. Comb. Theory. 4 (4): 376–390
Richard_K._Guy
Film and Television Centers NanoSystems Embedded Network Sensing Study of Women Chicano Studies Enormous Toroidal Plasma Device Film and Television Archive
History of San Jose State University
History_of_San_Jose_State_University
German American aerospace engineer (1912–1977)
constructed using rockets with recoverable and reusable ascent stages) was a toroid structure, with a diameter of 250 feet (76 m); this built on the concept
Wernher_von_Braun
Planar maps require at most four colors
required to color any map on a torus. This upper bound of 7 is sharp: certain toroidal polyhedra, such as the Szilassi polyhedron, require seven colors. A Möbius
Four_color_theorem
US organization to support traumatized children
Film and Television Centers NanoSystems Embedded Network Sensing Study of Women Chicano Studies Enormous Toroidal Plasma Device Film and Television Archive
National Child Traumatic Stress Network
National_Child_Traumatic_Stress_Network
American non-profit theatre company
Film and Television Centers NanoSystems Embedded Network Sensing Study of Women Chicano Studies Enormous Toroidal Plasma Device Film and Television Archive
Geffen_Playhouse
On tangency patterns of circles
itself to other objects embedded within the surface. An example comes from dessins d'enfant, a certain type of graph embedding used in algebraic geometry
Circle_packing_theorem
Public law school in Los Angeles, California
Film and Television Centers NanoSystems Embedded Network Sensing Study of Women Chicano Studies Enormous Toroidal Plasma Device Film and Television Archive
UCLA_Master_of_Legal_Studies
American ice hockey player and coach (born 1957)
Symmetric Torus McArdle Laboratory Morgridge Institute for Research Pegasus Toroidal Experiment UW Hospital & Clinics Viaspan WIYN Consortium WiCell Wisconsin
Mark_Johnson_(ice_hockey)
Laboratory school in Los Angeles, California, United States
Film and Television Centers NanoSystems Embedded Network Sensing Study of Women Chicano Studies Enormous Toroidal Plasma Device Film and Television Archive
UCLA_Lab_School
Building on the campus of the University of California, Los Angeles
Film and Television Centers NanoSystems Embedded Network Sensing Study of Women Chicano Studies Enormous Toroidal Plasma Device Film and Television Archive
Royce_Hall
Graduate professional school of the University of California, Los Angeles
Film and Television Centers NanoSystems Embedded Network Sensing Study of Women Chicano Studies Enormous Toroidal Plasma Device Film and Television Archive
UCLA School of Education and Information Studies
UCLA_School_of_Education_and_Information_Studies
TOROIDAL EMBEDDING
TOROIDAL EMBEDDING
TOROIDAL EMBEDDING
TOROIDAL EMBEDDING
Girl/Female
Hebrew
Light.
Girl/Female
Tamil
Courageous woman
Girl/Female
Arabic, Muslim, Sindhi
One who Speaks
Boy/Male
Arabic, Muslim
Decorated Throne
Girl/Female
Hindu, Indian, Marathi, Sanskrit
Singing
Girl/Female
Indian
Soaring Angel
Boy/Male
Tamil
Kirtin | கிரà¯à®¤à®¿à®¨
Celebrated
Boy/Male
Muslim
Faithful, Sincere
Boy/Male
Tamil
Visweswaran | விஸà¯à®µà¯‡à®¸à¯à®µà®°à®£
The great Lord for viswakarma
Boy/Male
Indian
Friendship, Kindness, Obligation
TOROIDAL EMBEDDING
TOROIDAL EMBEDDING
TOROIDAL EMBEDDING
TOROIDAL EMBEDDING
TOROIDAL EMBEDDING
a.
Nearly, but not exactly, conical.
a.
Of or pertaining to a zooid; as, a zooidal form.
a.
Resembling an egg in shape; egg-shaped; ovate; as, an ovoidal apple.
a.
Resembling a cone; conoidal.
a.
Spiral in arrangement or action.
a.
Turning the plane of polarization circularly or spirally to the right or left.
a.
Shaped like an egg.
a.
Having the power to produce a purple color; as, the purpurogenous membrane, or choroidal epithelium, of the eye. See Visual purple, under Visual.
p. pr. & vb. n.
of Embed
a.
Pertaining to the choroid coat.
a.
Alt. of Ovoidal
n.
The act of embedding, or the state of being embedded.
a.
Having the planes arranged spirally, so that they incline all to the right (or left) of a vertical line; -- said of certain hemihedral forms.
a.
Same as Conoidal.