如图，在三棱柱\(ABC-A _{1} B _{1} C _{1}\)中，侧面\(ABB _{1} A _{1}\)和侧面\(BCC _{1} B _{1}\)都是边长为\(2\)的菱形，且\(∠BAA _{1} =∠CBB _{1} = \dfrac {π}{3}\)．
\((\)Ⅰ\()\)证明：\(BB _{1} ⊥A _{1} C\)；
\((\)Ⅱ\()\)若\(A _{1} C= \sqrt {6} .\)求三棱柱\(ABC-A _{1} B _{1} C _{1}\)的体积．