@misc{Lutz, author = {Lutz, Frank H.}, title = {Enumeration and Random Realization of Triangulated Surfaces}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9012}, number = {06-07}, abstract = {We discuss different approaches for the enumeration of triangulated surfaces. In particular, we enumerate all triangulated surfaces with 9 and 10 vertices. We also show how geometric realizations of orientable surfaces with few vertices can be obtained by choosing coordinates randomly.}, language = {en} } @misc{Lutz, author = {Lutz, Frank H.}, title = {Triangulated Manifolds with Few Vertices: Combinatorial Manifolds}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9028}, number = {06-08}, abstract = {In this survey on combinatorial properties of triangulated manifolds we discuss various lower bounds on the number of vertices of simplicial and combinatorial manifolds. Moreover, we give a list of all known examples of vertex-minimal triangulations.}, language = {en} } @misc{HougardyLutzZelke, author = {Hougardy, Stefan and Lutz, Frank H. and Zelke, Mariano}, title = {Polyhedra of Genus 2 with 10 Vertices and Minimal Coordinates}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9054}, number = {06-12}, abstract = {We give coordinate-minimal geometric realizations in general position of all 865 vertex-minimal triangulations of the orientable surface of genus 2 in the 4x4x4-cube.}, language = {en} } @misc{HougardyLutzZelke, author = {Hougardy, Stefan and Lutz, Frank H. and Zelke, Mariano}, title = {Polyhedra of Genus 3 with 10 Vertices and Minimal Coordinates}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9064}, number = {06-13}, abstract = {We give coordinate-minimal geometric realizations in general position for 17 of the 20 vertex-minimal triangulations of the orientable surface of genus 3 in the 5x5x5-cube.}, language = {en} }