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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
In geometry, a toroidal polyhedron is a polyhedron which is also a toroid (a g-holed torus), having a topological genus (g) of 1 or greater. Notable examples
Toroidal_polyhedron
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
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
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
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 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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Number of "holes" of a surface
orientable surfaces Planar graph: genus 0 Toroidal graph: genus 1 Philadelphia Pretzel graph: Double Toroidal graph: genus 2 Standard Pretzel graph: genus
Genus_(mathematics)
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
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
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
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
Stadium 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
Easton_Stadium
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
Process of combining atomic nuclei
it are magnetic confinement (toroid designs) and inertial confinement (laser designs). Workable designs for a toroidal reactor that theoretically will
Nuclear_fusion
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
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
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
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
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
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
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
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
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
Comparison of a large range of energies
Takiwaki, Tomoya (1 February 2021). "Extremely Energetic Supernova Explosions Embedded in a Massive Circumstellar Medium: The Case of SN 2016aps". The Astrophysical
Orders_of_magnitude_(energy)
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
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
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
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
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
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
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
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
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
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
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
Industrial process based on lost-wax casting
investment cast for a titanium space bus with integral propellant tank and embedded cable routing. Engineering portal Full-mold casting Lost-foam casting "Investment
Investment_casting
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
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
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
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
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
Public health school at 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 Fielding School of Public Health
UCLA_Fielding_School_of_Public_Health
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
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
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
Student newspaper of UCLA
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Daily_Bruin
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
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
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
Linguistic database
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UCLA Phonological Segment Inventory Database
UCLA_Phonological_Segment_Inventory_Database
American public research university
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University of California, Los Angeles
University_of_California,_Los_Angeles
2024 occupation protest in Los Angeles, California
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2024 University of California, Los Angeles pro-Palestinian campus occupation
2024_University_of_California,_Los_Angeles_pro-Palestinian_campus_occupation
Baseball team representing the University of California, Los Angeles
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UCLA_Bruins_baseball
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
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
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
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History of San Jose State University
History_of_San_Jose_State_University
Healthcare network in California, United States
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UCLA_Health
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
Graphical representation of energy flows in physical systems
representation contains the constitutive equations of each component, embedded in the structure of bond and junctions. The question of how to manipulate
Bond_graph
Dental school in Los Angeles, California, US
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Public law school in Los Angeles, California
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UCLA Asian American Studies Center
UCLA_Asian_American_Studies_Center
TOROIDAL EMBEDDING
TOROIDAL EMBEDDING
TOROIDAL EMBEDDING
TOROIDAL EMBEDDING
Boy/Male
Tamil
Shanmith | ஷாநà¯à®®à®¿à®¤
Male
Hebrew
(×Ö²×—Ö´×™×Ö¸×) Hebrew name ACHIYAM means "mother's brother," i.e. "uncle." In the bible, this is the name of one of King David's warriors.
Male
English
 Short form of English Zachary, ZACH means "whom Jehovah remembered." Compare with another form of Zach.
Boy/Male
Indian
The protecting friend
Boy/Male
Hindu, Indian, Kannada, Telugu, Traditional
Merciful
Girl/Female
Gujarati, Indian, Tamil
Hindu Month Name
Boy/Male
Indian
A companion of prophet Muhammad
Girl/Female
Hindu
Name of Hindu Goddess Lakshmi ji
Boy/Male
Hindu
Full of strength
Girl/Female
Arabic, Muslim
Look After
TOROIDAL EMBEDDING
TOROIDAL EMBEDDING
TOROIDAL EMBEDDING
TOROIDAL EMBEDDING
TOROIDAL EMBEDDING
a.
Same as Conoidal.
a.
Shaped like an egg.
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.
Turning the plane of polarization circularly or spirally to the right or left.
a.
Of or pertaining to a zooid; as, a zooidal form.
a.
Nearly, but not exactly, conical.
a.
Alt. of Ovoidal
a.
Resembling a cone; conoidal.
a.
Having the power to produce a purple color; as, the purpurogenous membrane, or choroidal epithelium, of the eye. See Visual purple, under Visual.
n.
The act of embedding, or the state of being embedded.
a.
Pertaining to the choroid coat.
a.
Resembling an egg in shape; egg-shaped; ovate; as, an ovoidal apple.
p. pr. & vb. n.
of Embed
a.
Spiral in arrangement or action.