**Category:** Geometry  
**Subtype:** Solid Geometry (specifically, pyramids)  
**Problem Description:** Calculate the volume \(V\) of a pyramid (or tetrahedron) \(S.ABC\) where the base \(ABC\) is an isosceles right triangle with legs of length \(a\), and the apex \(S\) forms an equilateral triangle with the base edge \(AB\) and is perpendicular to the base.