We investigate several families of polyhedra defining nested refinement domains for hierarchies generated through longest edge tetrahedral bisection. We define the descendant domain of a tetrahedron as the domain covered by all possible descendants generated by conforming bisections. Due to the fractal nature of these shapes, we propose two simpler approximations to the descendant domain that are relatively tight with respect to the descendant domain and can be implicitly computed at runtime. We conclude with a brief discussion of the applications of these shapes for interactive view-dependent volume visualization and isosurface extraction.