The taxicab space group

GELİŞGEN Ö., Kaya R.

ACTA MATHEMATICA HUNGARICA, vol.122, pp.187-200, 2009 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 122
  • Publication Date: 2009
  • Doi Number: 10.1007/s10474-008-8006-9
  • Journal Name: ACTA MATHEMATICA HUNGARICA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.187-200
  • Keywords: group, isometry, metric, taxicab metric, taxicab geometry
  • Eskisehir Osmangazi University Affiliated: Yes

Abstract

It is shown that the group of isometries of the 3-dimensional space with respect to taxicab metric is the semi-direct product of octahedral group O (h) and T(3), where O (h) is the (Euclidean) symmetry group of the regular octahedron and T(3) is the group of all translations of the 3-dimensional space.