1. In a tetrahedron with four vertices of a rectangular prism as its vertices, the number of tetrahedra where all four faces are right-angled triangles is ( ).
(A) 8
(B) 16
(C) 24
(D) 48
-、1.C.
It is known that there is a one-to-one correspondence between a tetrahedron satisfying the condition and a pair of skew lines among the edges of a rectangular parallelepiped. Since there are $\frac{6 \times 8}{2}=24$ pairs of skew lines among the edges of the rectangular parallelepiped, the number of tetrahedra sought is 24.