Regular map

English

Noun

1. Template:Lb A morphism between algebraic varieties.
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   • 2017, José F. Fernando, José M. Gamboa, Carlos Ueno, Polynomial, regular and Nash images of Euclidean spaces, Fabrizio Broglia, Françoise Delon, Max Dickmann, Danielle Gondard-Cozette, Victoria Ann Powers (editors), Ordered Algebraic Structures and Related Topics: International Conference, Template:W, page 160,

     The 1-dimensional semialgebraic set $𝒮:=x>0,xy=1$ is the image of the regular map

     $f:{ℝ}^2\to {ℝ}^2,(x,y)\mapsto ((xy-1{)}^2+x^2,\frac{1}{(xy-1{)}^2+x^2})$.

2. Template:Lb A symmetric tessellation of a closed surface; a decomposition of a two-dimensional manifold into topological disks such that every flag (incident vertex-edge-face triple) can be transformed into any other flag by a symmetry (i.e., an automorphism) of the decomposition.
   • 1990 [McGraw-Hill], Jay Kappraff, Connections: The Geometric Bridge Between Art and Science, 2001, World Scientific, page 141,

     Just as there are only five regular maps on the sphere (or plane), there are only three classes of regular maps that can be created on a torus.

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   • 2013, Roman Nedela, Martin Škoviera, 7.6: Maps, Jonathan L. Gross, Jay Yellen, Ping Zhang (editors), Handbook of Graph Theory, 2nd Edition, CRC Press, page 845,

     If $M$ is a regular map of type $\{p,q\}$, then $𝐴𝑢𝑡(M)\approx \mathrm{\Delta }(p,q,2)/N$ for some normal subgroup $N⊴\mathrm{\Delta }(p,q,2)$. Similar statements hold for the class of orientably regular maps and subgroups of ${\mathrm{\Delta }}^{+}$ and ${\mathrm{\Delta }}^{+}(p,q,2)$.

Synonyms

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