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Topics referred to by the same term
Regular map may refer to: a regular map (algebraic geometry), in algebraic geometry, an everywhere-defined, polynomial function of algebraic varieties
Regular_map
Symmetric tessellation of a closed surface
In mathematics, a regular map is a symmetric tessellation of a closed surface. More precisely, a regular map is a decomposition of a two-dimensional manifold
Regular_map_(graph_theory)
Concept in mathematics
regular map. A morphism from an algebraic variety to the affine line is also called a regular function. A regular map whose inverse is also regular is
Morphism of algebraic varieties
Morphism_of_algebraic_varieties
Topics referred to by the same term
bricks Regular map (algebraic geometry), a map between varieties given by polynomials Regular point, a non-singular point of an algebraic variety Regular point
Regular
Web mapping service
no more than three years old and is updated on a regular basis, according to a 2011 report. Google Maps previously used a variant of the Mercator projection
Google_Maps
Symbolic depiction of spatial relationships
decisions when designing a map, including the map scale, coordinate system, symbols, colors, labels, and typography. The selection of a map projection is a critical
Map
In mathematics, a Cauchy-continuous, or Cauchy-regular, function is a special kind of continuous function between metric spaces (or more general spaces)
Cauchy-continuous_function
Branch of mathematics
a regular map from V to V′ if the range of f is contained in V′. The definition of the regular maps apply also to algebraic sets. The regular maps are
Algebraic_geometry
Map that uses pictures to represent features
landscape features in perspective. While regular maps focus on the accurate rendition of distances, pictorial maps enhance landmarks and often incorporate
Pictorial_map
Polyhedron with regular congruent polygons as faces
A regular polyhedron is a polyhedron with regular and congruent polygons as faces. Its symmetry group acts transitively on its flags. A regular polyhedron
Regular_polyhedron
Function, homomorphism, or morphism
operation is composition of permutations Regular map (algebraic geometry) – Morphism of algebraic varieties The words map, mapping, correspondence, and operator
Map_(mathematics)
Map of a planet's gravity levels and anomalies
conducted at regular intervals. For surface mapping of gravity, placement of instruments can be randomized. Surface gravity mapping is often used to map out gravity
Gravity_map
Map application operated by Apple
competitor Google Maps, which allowed the application to use less data than Google Maps. The map has four available layers: regular map, satellite view
Apple_Maps
Mathematics of smooth surfaces
U ′ of a regular surface, the composition f −1 ∘ f ′ is necessarily smooth as a map between open subsets of ℝ2. This shows that any regular surface naturally
Differential geometry of surfaces
Differential_geometry_of_surfaces
Planar maps require at most four colors
connected open subset of the plane) is not the same as that of "country" on regular maps, since a country need not be contiguous: it may have exclaves, like Angola
Four_color_theorem
Concept in algebraic geometry
morphism between two affine varieties X , Y {\displaystyle X,Y} is a dense regular map which induces isomorphic inclusion k [ Y ] ↪ k [ X ] {\displaystyle
Finite_morphism
Type of continuous map in topology
the map p : C × → C × {\displaystyle p:\mathbb {C} ^{\times }\to \mathbb {C} ^{\times }} with p ( z ) = z n {\displaystyle p(z)=z^{n}} is a regular cover
Covering_space
Study and creation of maps of imagined places or events
[regular] map re-presents what is already there; a fictional map is often primary – to create the map means, largely, to create the world of the map."
Fantasy_cartography
Simple polynomial map exhibiting chaotic behavior
\infty )} changes dynamics from regular to chaotic one with qualitatively the same bifurcation diagram as those for logistic map. The Feigenbaum constants can
Logistic_map
Map subdivided into a hexagonal tiling, small regular hexagons of identical size
video games. A hex map is subdivided into a hexagonal tiling, small regular hexagons of identical size. The primary advantage of a hex map over a traditional
Hex_map
This article lists the regular polytopes in Euclidean, spherical and hyperbolic spaces. This table shows a summary of regular polytope counts by rank.
List_of_regular_polytopes
Cubic graph with 10 vertices and 15 edges
construction forms a regular map and shows that the Petersen graph has non-orientable genus 1. The Petersen graph is strongly regular (with signature srg(10
Petersen_graph
module E over a commutative ring A, an A-linear map u : E → A {\displaystyle u:E\to A} is called Koszul-regular if the Koszul complex determined by it is acyclic
Regular_embedding
Topics referred to by the same term
synonym for an associative array. A finite map in algebraic geometry is a regular map such that the preimage of any point is a finite set, plus a closedness
Finite_map
Systematic representation of the surface of a sphere or ellipsoid onto a plane
a map projection is any of a broad set of transformations employed to represent the curved two-dimensional surface of a globe on a plane. In a map projection
Map_projection
Solid with twenty equal triangular faces
cartography, R. Buckminster Fuller used the net of a regular icosahedron to create a map known as Dymaxion map, by subdividing the net into triangles, followed
Regular_icosahedron
Schematic transport map of the London Underground network
individual companies' routes. The maps were not typically schematic and were simply the line overlaid on a regular city map. There was no integration of the
Tube_map
Graph drawing used to study Riemann surfaces
set of triangles generated in this way starting from a regular dodecahedron. When the regular map lies in a surface whose genus is greater than one, the
Dessin_d'enfant
Solid with four equal triangular faces
A regular tetrahedron is a polyhedron with four equilateral triangular faces. A regular tetrahedron is a tetrahedron (that is, a four-sided polyhedron)
Regular_tetrahedron
mathematics, specifically algebraic geometry, an exceptional divisor for a regular map f : X → Y {\displaystyle f:X\rightarrow Y} of varieties is a kind of
Exceptional_divisor
Undirected graph with 14 vertices
is the regular map {6,3}2,1, with 7 hexagonal faces. Each face of the map is adjacent to every other face, thus as a result coloring the map requires
Heawood_graph
Solid with eight equal triangular faces
more generally, a regular polyhedron. If the faces are isosceles triangles, the regular octahedron becomes a square bipyramid. The regular octahedron is an
Regular_octahedron
G} at a regular central value p ∈ Z ( g ∗ ) {\displaystyle p\in Z({\mathfrak {g}}^{*})} of μ {\displaystyle \mu } . It is defined as the map of equivariant
Kirwan_map
Swiss geological survey
and St. Moritz. These maps cost CHF 13.50 each (2004). 208 maps on this scale are published at regular intervals. The first map published on this scale
Swisstopo
Representation theory of groups
regular representation ρ, an inversion must occur in order to satisfy the axioms of a representation. Specifically, given g ∈ G, ρg is the linear map
Regular_representation
One of two different regular graphs with 16 vertices
hypercubes no two of which meet face-to-face. The 5-regular Clebsch graph can be embedded as a regular map in the orientable manifold of genus 5, forming pentagonal
Clebsch_graph
of the Gauss map, with here k partial derivatives not vanishing. More precisely, the set I ( n , k ) {\displaystyle I(n,k)} of regular homotopy classes
Regular_homotopy
McGibbon 1993). Similar constructions are defined for maps of spectra. Let α {\displaystyle \alpha } be a regular cardinal. A morphism f : x → y {\displaystyle
Phantom_map
"Regular Series" trench map. These Regular Series maps, printed in Britain, did much to improve the situation (all 1:10,000 scale maps in this series, printed
Trench_map
label that would lead back to v {\displaystyle v} . For a D-regular graph G, the rotation map R o t G : [ N ] × [ D ] → [ N ] × [ D ] {\displaystyle \mathrm
Rotation_map
Algebraic variety defined within an affine space
topology on An × Am , but not in the product topology. A morphism, or regular map, of affine varieties is a function between affine varieties that is polynomial
Affine_variety
History and style of cartography in Japan
depicted area is an important characteristic of traditional Japanese maps, as is the regular inclusion of text, as text and image were not separated in Japan
Japanese_maps
Concept in topology
the degree of a smooth map can be defined as follows: If f is a smooth map whose domain is a compact manifold and p is a regular value of f, consider the
Degree of a continuous mapping
Degree_of_a_continuous_mapping
subsets 2. A birational map is a rational map with rational "inverse" biregular 1. A biregular map is a regular map with regular inverse 2. Two varieties
Glossary of classical algebraic geometry
Glossary_of_classical_algebraic_geometry
Types of interactive mapping services
collected by sensors and the maps are generated or updated at regular intervals or on demand. Animated maps show changes in the map over time by animating one
Web_mapping
2018 video game
represent Alcatraz Island. Main differences between Alcatraz and the regular map include the fact that only 40 players are allowed per match, there are
Call_of_Duty:_Black_Ops_4
shears, and other similarities and some, but not all linear maps. All triangles are affine-regular. In other words, all triangles can be generated by applying
Affine-regular_polygon
Injective polynomial functions are bijective
n {\displaystyle \mathbb {C} ^{n}} . The full theorem generalizes to regular maps on any algebraic variety over an algebraically closed field. Grothendieck's
Ax–Grothendieck_theorem
Map used in orienteering
typically topographic maps from the national mapping agency. While national mapping agencies update their topographic maps on a regular basis, they are usually
Orienteering_map
Poset representing certain properties of a polytope
the dual of the facet to which V maps in the dual polytope. Formally, an abstract polytope is defined to be regular if its automorphism group acts transitively
Abstract_polytope
Symmetric bipartite cubic graph with 16 vertices and 24 edges
flag graph of the genus 2 regular map having Möbius–Kantor graph as a skeleton. This means it can be obtained from the regular map as a skeleton of the dual
Möbius–Kantor_graph
map projections that have articles of their own on Wikipedia or that are otherwise notable. Because there is no limit to the number of possible map projections
List_of_map_projections
Map of radio signal strength in an area
a regular grid. The types of signal strength maps, presented below, are determined by the signal strength metric that they provide. In coverage maps, γ
Radio_map
2003 video game
become regular map squares when destroyed. Removing all of the Geo Panels from a map will cause a blast of energy which hurts all enemies on the map and
Disgaea:_Hour_of_Darkness
Functions that send open (resp. closed) subsets to open (resp. closed) subsets
mathematics, more specifically in topology, an open map is a function between two topological spaces that maps open sets to open sets. That is, a function f
Open_and_closed_maps
Well-behaved sequence in a commutative ring
m. Then any elements r1, ..., rd of m which map to a basis for m/m2 as an R/m-vector space form a regular sequence. An important case is when the depth
Regular_sequence
Compact Riemann surface of genus 3
The Klein quartic admits tilings connected with the symmetry group (a "regular map"), and these are used in understanding the symmetry group, dating back
Klein_quartic
Concept in the mathematics of paper folding
In the mathematics of paper folding, map folding and stamp folding are two problems of counting the number of ways that a piece of paper can be folded
Map_folding
Continuous closed surjective map, each of whose fibers are also compact sets
{\displaystyle p\colon X\to Y} is a perfect map and X {\displaystyle X} is regular, then Y {\displaystyle Y} is regular. (If p {\displaystyle p} is merely continuous
Perfect_map
W ⊆ A m {\displaystyle W\subseteq \mathbb {A} ^{m}} and a dominant regular map ϕ : V → W {\displaystyle \phi \colon V\to W} , the induced homomorphism
Finite_algebra
Places where the globe has been split in a map projection
globe gores have been developed in order to paste map sections onto model globes. These are regular interruption either along the equator, or in polar
Interruption_(map_projection)
Distributed data processing framework
CouchDB, a database that uses JSON for documents, JavaScript for MapReduce queries, and regular HTTP for an API Big data Data-intensive computing HPCC – LexisNexis
Apache_Hadoop
Polygon with one edge and one vertex
Digon Coxeter, Introduction to geometry, 1969, Second edition, sec 21.3 Regular maps, p. 386-388 Herbert Busemann, The geometry of geodesics. New York, Academic
Monogon
Discrete-time dynamical system
diagram. If b is held constant (e.g., at 0.3) and a is varied, the map transitions from regular (periodic) to chaotic behavior. This transition occurs through
Hénon_map
Type of map projection
can be applied to any polyhedron with regular faces. The projection used in later versions of the Dymaxion map can be generalized to other equilateral
Polyhedral_map_projection
Algebraic variety with a group structure
k ) {\displaystyle e\in \mathrm {G} (k)} (the neutral element), and regular maps G × G → G {\displaystyle \mathrm {G} \times \mathrm {G} \to \mathrm {G}
Algebraic_group
Undirected graph named after S. S. Shrikhande
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 torus) is the
Shrikhande_graph
Partition of a sphere's surface into polygons
Projective Regular Polytopes". Abstract Regular Polytopes. Cambridge University Press. pp. 162–5. ISBN 0-521-81496-0. Coxeter, H.S.M. (1969). "§21.3 Regular maps'"
Spherical_polyhedron
Image also containing data on distances of objects from the camera
In 3D computer graphics and computer vision, a depth map is an image or image channel that contains information relating to the distance of the surfaces
Depth_map
Continent
Schengen Area, have also abolished internal border and immigration controls. Regular popular elections take place every five years within the EU; they are considered
Europe
Type of cardinal number in mathematics
a regular cardinal is a cardinal number that is equal to its own cofinality. More explicitly, this means that κ {\displaystyle \kappa } is a regular cardinal
Regular_cardinal
Polytope with highest degree of symmetry
face) can be mapped to any other such flag by a suitable symmetry of the cube. Thus we can define a regular polytope very succinctly: A regular polytope is
Regular_polytope
(x-3)(x+3)(x^{4}-5x^{2}+3)^{6}.\,} The F26A graph can be embedded as a chiral regular map in the torus, with 13 hexagonal faces. The dual graph for this embedding
F26A_graph
Topology on prime ideals and algebraic varieties
so every variety satisfies the T 1 {\displaystyle T_{1}} axiom. Every regular map of varieties is continuous in the Zariski topology. In fact, the Zariski
Zariski_topology
Board game
(C)rypt spaces in the underworld yield additional gameplay bonuses on the regular map. The wild cards are removed from the Territory deck. The Miracle and
Risk_Godstorm
Tool in symplectic geometry
mathematics, specifically in symplectic geometry, the momentum map (or, by false etymology, moment map) is a tool associated with a Hamiltonian action of a Lie
Momentum_map
Embedding a graph in a topological space, often Euclidean
edge list, a data structure to represent a graph embedding in the plane Regular map (graph theory) Fáry's theorem, which says that a straight line planar
Graph_embedding
Graphic depiction of a geographic phenomenon
A map symbol or cartographic symbol is a graphical device used to visually represent a real-world feature on a map, working in the same fashion as other
Map_symbol
Algebraic variety
field such that through every two points there passes the image of a regular map from the projective line into V. Equivalently, a variety is rationally
Rational_variety
Map distorting size to show another value
cartogram (also called a value-area map or an anamorphic map, the latter common among German speakers) is a thematic map of a set of features (countries,
Cartogram
Professional soccer league in the United States and Canada
and Major League Baseball (MLB) with over 26,000 fans per game. The MLS regular season typically starts in late February and runs through mid-October,
Major_League_Soccer
Thread safe Map collections for concurrency in Java
implements the original regular single-threaded maps, and also new thread-safe maps implementing the java.util.concurrent.ConcurrentMap interface among other
Java_ConcurrentMap
Grothendieck ring is a Noetherian ring such that the map of any of its local rings to the completion is regular (defined below). Almost all Noetherian rings that
G-ring
Aspect of topological graph theory
group of these operations. Applying the Petrie dual to a regular polyhedron produces a regular map. The number of skew h-gonal faces is g/2h, where g is
Petrie_dual
Long exact sequence
the cup product, and the pushforward map no longer corresponds to integration. Let i: X → Y be a (closed) regular embedding of codimension d, Y' → Y a
Gysin_homomorphism
Concept in algebraic geometry
X is regular, and transverse to the exceptional locus of the resolution morphism (so in particular it resolves the singularities of X). The map from the
Resolution_of_singularities
Graph in which all ordered pairs of linked nodes are automorphic
there are none for t ≥ 6. Algebraic graph theory Gallery of named graphs Regular map Biggs, Norman (1993). Algebraic Graph Theory (2nd ed.). Cambridge: Cambridge
Symmetric_graph
Graph property
In the mathematical field of graph theory, a distance-regular graph is a regular graph such that for any two vertices v and w, the number of vertices at
Distance-regular_graph
Bipartite, 3-regular undirected graph
self-Petrie dual regular map with nine hexagonal faces; the second, to form a regular map with 18 triangular faces. The two regular toroidal maps are dual to
Pappus_graph
Method to draw shadows in computer graphic images
to create a shadow map. The light's view is rendered, storing the depth of every surface it sees (the shadow map). Next, the regular scene is rendered
Shadow_mapping
North American professional baseball league
were the home team in a regular-season two-game series against the New York Yankees. The games, which were the first regular-season MLB games held in
Major_League_Baseball
Mathematical object studied in the field of algebraic geometry
V1 ≅ V2, if there are regular maps φ : V1 → V2 and ψ : V2 → V1 such that the compositions ψ ∘ φ and φ ∘ ψ are the identity maps on V1 and V2 respectively
Algebraic_variety
Concept in mathematics
physics was to use either conformal or harmonic mapping to generate regular grids. A map u : M → N {\displaystyle u:M\rightarrow N} between Riemannian manifolds
Harmonic_map
Type of algebra
V} ; moreover, if ϕ : V → W {\displaystyle \phi \colon V\to W} is a regular map between the affine algebraic sets V ⊆ A n {\displaystyle V\subseteq \mathbb
Finitely_generated_algebra
Polyhedron with non-planar faces
{l, m |, q}. These can also be represented a regular finite map or {l, m}2q, and group Gl,m,q. Regular skew polyhedra can also be constructed in dimensions
Regular_skew_polyhedron
Plane tiling corresponding to a polyhedron
Coxeter, Introduction to geometry, 1969, Second edition, sec 21.3 Regular maps, p. 386-388 Archdeacon, Dan; Negami, Seiya (1993), "The construction
Projective_polyhedron
Distance-transitive cubic graph with 20 nodes and 30 edges
distance-regular graphs are known. The Desargues graph is one of the 13 such graphs. The Desargues graph can be embedded as a self-Petrie dual regular map in
Desargues_graph
About polynomials in several variables
n → K n {\displaystyle G:\mathbb {K} ^{n}\to \mathbb {K} ^{n}} that is regular, meaning its components are polynomials. The condition J F ≠ 0 {\displaystyle
Jacobian_conjecture
Regular tiling of the hyperbolic plane
[(4,4,4)] symmetry. The regular map {8,3}2,0 can be seen as a 6-coloring of the {8,3} hyperbolic tiling. Within the regular map, octagons of the same color
Octagonal_tiling
Type of polyhedron with many holes
Bokowski, Jürgen; H., Kevin (2025). "Polyhedral Embeddings of Triangular Regular Maps of Genus g {\displaystyle g} , 2 ≤ g ≤ 14 {\displaystyle 2\leq g\leq
Leonardo_polyhedron
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