regular map

Noun

 * 1)  A morphism between algebraic varieties.
 * 2) * 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,, page 160,
 * The 1-dimensional semialgebraic set $$\mathcal{S}:={x>0,xy=1}$$ is the image of the regular map
 * $$f: \R^2\rightarrow \R^2, (x,y)\mapsto \left ((xy-1)^2+x^2, \frac{1}{(xy-1)^2+x^2}\right )$$.
 * 1)  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.
 * 2) * 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.
 * 1) * 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 $$\mathit{Aut}(M)\approx\Delta(p,q,2)/N$$ for some normal subgroup $$N\ \trianglelefteq\ \Delta(p,q,2)$$. Similar statements hold for the class of orientably regular maps and subgroups of $$\Delta^+$$ and $$\Delta^+(p,q,2)$$.
 * 1) * 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 $$\mathit{Aut}(M)\approx\Delta(p,q,2)/N$$ for some normal subgroup $$N\ \trianglelefteq\ \Delta(p,q,2)$$. Similar statements hold for the class of orientably regular maps and subgroups of $$\Delta^+$$ and $$\Delta^+(p,q,2)$$.
 * If $$M$$ is a regular map of type $$\{p, q\}$$, then $$\mathit{Aut}(M)\approx\Delta(p,q,2)/N$$ for some normal subgroup $$N\ \trianglelefteq\ \Delta(p,q,2)$$. Similar statements hold for the class of orientably regular maps and subgroups of $$\Delta^+$$ and $$\Delta^+(p,q,2)$$.