International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 58479, 7 pages
doi:10.1155/IJMMS/2006/58479
Mappings which preserve regular dodecahedrons
Mathematics Section, College of Science and Technology, Hong-Ik University, Chochiwon 339-701, South Korea
Received 4 June 2006; Accepted 5 July 2006
Copyright © 2006 Byungbae Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We prove that if a one-to-one mapping f:ℝ3→ℝ3 preserves regular dodecahedrons, then f is a linear isometry up to translation.