Aplicações da Trigonometria Esférica em problemas da Simetria Cristalográfica

Resumo

The present article deals with the application of elementary spherical trigonometry to solution of symmetry problems. The main purpose of the article is to point out symmetry axis associations, and to show the possibilities and impossibilities of several associations, revealed through spherical trigonometric relations. The following axis associations have been a matter of study : a ) 6 + 6; b ) 4 + 4; c ) 2 + 2; d ) 6 + 3; e ) 6 + 4; f ) 6 + 2; g ) 4 + 3. For solution of all the proposed problem sonly one trigonometric formula has been used: cos a = cos b cos c + sen b sen c cos A which is applicable to scalene triangles