Fan triangulations of a hyperbolic plane of positive curvatureстатья
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Дата последнего поиска статьи во внешних источниках: 21 сентября 2017 г.
Аннотация:We study the families (ℱλ) of normal partitions of a 3-(1)-contour F of a hyperbolic plane H^ of positive curvature into simple 4-contours whose hyperbolic diagonal lines are parallel to the base of F. A 3-(1)-contour with a given partition from a family (ℱλ) (or some its normal subpartition) is called a fan. We construct fan partitions Pe, Ph, and Pp of H^ whose symmetry groups are generated by a shift along an elliptic (respectively, hyperbolic and parabolic) straight line. It is proved that the partitions Ph and Pp are normal. The partitions Ph and Pp whose cells are trihedrals present examples of the first triangulations of H^.