7 papers · 1 filter
On the m-point convexity
Wenzhi Liu, Wei Wang, Liping Yuan +1
Let . A set is said to be -point convex, if for every distinct points in , at least one of the line-segments determined by them lie…
The orthogonal connectedness of polyhedral surfaces
Julia Q. Du, Xuemei He, Xiaotian Song +3
Using the orthogonal connectedness, we introduce the notion of orthogonal decomposability of convex polytopes and study it in the case of Platonic and Archimedean solids. While doi…
Excursions in Sylvester-Gallai land
Imre Barany, Julia Q. Du, Dan Schwarz +2
The Sylvester-Gallai theorem states that for a finite set of points in the plane, if every line determined by any two of these points also contains a third, then the set is necessa…
Orthogonally connected sets
Xuemei He, Xiaotian Song, Liping Yuan +1
In this paper, we further investigate the orthogonally connected sets and establish necessary and sufficient conditions for a set to be staircase connected.
A note on discrete lattice-periodic sets with an application to Archimedean tilings
Matthias Schymura, Liping Yuan
Cao & Yuan obtained a Blichfeldt-type result for the vertex set of the edge-to-edge tiling of the plane by regular hexagons. Observing that every Archimedean tiling is the union of…
Volumes of convex lattice polytopes and a question of V. I. Arnold
Imre Barany, Liping Yuan
We show by a direct construction that there are at least convex lattice polytopes in of volume that are different in the sense that no…
Acute Triangulations of the Cuboctahedral Surface
Xiao Feng, Liping Yuan
In this paper we prove that the surface of the cuboctahedron can be triangulated into 8 non-obtuse triangles and 12 acute triangles. Furthermore, we show that both bounds are the b…