The aim of this paper is to investigate rotated versions of the densest known lattices in dimensions 2, 3, 4, 5, 6, 7, 8, 12 and 24 constructed via ideals and free Z-modules that are not ideals in subfields of cyclotomic fields. The focus is on totally real number fields and the associated full diversity lattices which may be suitable for signal transmission over both Gaussian and Rayleigh fading channels. We also discuss on the existence of a number field K such that it is possible to obtain the lattices A(2), E-6 and E-7 via a twisted embedding applied to a fractional ideal of O-K. (C) 2015 Elsevier Inc. All rights reserved.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Univ Fed Sao Paulo, UNIFESP, BR-12247014 Sao Jose Dos Campos, SP, BrazilSao Paulo State Univ, UNESP, BR-15054000 Sao Jose Do Rio Preto, SP, BrazilUniv Estadual Campinas, UNICAMP, BR-13083859 Campinas, SP, BrazilUniv Estadual Campinas, UNICAMP, BR-13484350 Limeira, SP, BrazilSao Paulo State Univ, UNESP, BR-15054000 Sao Jose Do Rio Preto, SP, BrazilCNPq: 150802/2012-9CNPq: 312926/2013-8FAPESP: 2013/25977-7