TY - JOUR
T1 - Balanced triangulations
AU - Jia, Lijie
AU - Yuan, Liping
AU - Zamfirescu, Carol T.
AU - Zamfirescu, Tudor I.
PY - 2013/10/28
Y1 - 2013/10/28
N2 - Motivated by applications in numerical analysis, we investigate balanced triangulations, i.e. triangulations where all angles are strictly larger than pi/6 and strictly smaller than pi/2, giving the optimal lower bound for the number of triangles in the case of the square. We also investigate platonic surfaces, where we find for each one its respective optimal bound. In particular, we settle (affirmatively) the open question whether there exist acute triangulations of the regular dodecahedral surface with 12 acute triangles [J. Itoh, T. Zamfirescu, Acute triangulations of the regular dodecahedral surface, European J. Combin. 28 (2007) 1072-1086]. (C) 2013 Elsevier B.V. All rights reserved.
AB - Motivated by applications in numerical analysis, we investigate balanced triangulations, i.e. triangulations where all angles are strictly larger than pi/6 and strictly smaller than pi/2, giving the optimal lower bound for the number of triangles in the case of the square. We also investigate platonic surfaces, where we find for each one its respective optimal bound. In particular, we settle (affirmatively) the open question whether there exist acute triangulations of the regular dodecahedral surface with 12 acute triangles [J. Itoh, T. Zamfirescu, Acute triangulations of the regular dodecahedral surface, European J. Combin. 28 (2007) 1072-1086]. (C) 2013 Elsevier B.V. All rights reserved.
KW - Acute triangulations
KW - Balanced triangulations
KW - Platonic solids
UR - https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=web_of_science_starterapi&SrcAuth=WosAPI&KeyUT=WOS:000323867400016&DestLinkType=FullRecord&DestApp=WOS_CPL
U2 - 10.1016/j.disc.2013.05.017
DO - 10.1016/j.disc.2013.05.017
M3 - Article
SN - 0012-365X
VL - 313
SP - 2178
EP - 2191
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 20
ER -