You can find the construction of the triple covering for the alternating group $\mathbb{A}_6$ in Chapter 2, Section 7.3 of Wilson's book:

Wilson, Robert A. The finite simple groups. Graduate Texts in Mathematics, 251. Springer-Verlag London, Ltd., London, 2009. xvi+298 pp. ISBN: 978-1-84800-987-5 MR2562037 (2011e:20018)

[Here][1] you have the link to the page you are looking for (Google books). 


  [1]: http://books.google.com.ar/books?id=lYMAg_Sj7hUC&lpg=PR9&pg=PA29#v=onepage&q&f=false