And Pythagorean theorem, AC=CF=FA=2√2, ∴ACF is a regular triangle. It is proved that the vector obtained by connecting the center of triangle with m is perpendicular to the base.

Taking D as the origin, a rectangular coordinate system is established, with DA as the X axis, DC as the Y axis and DE as the Z axis. There are:

A(2，0，0)、C(0，2，0)、F(2，2，2)。

∴ Central coordinates (4/3, 4/3, 2/3).

Let M(x, x, z),

The vector GM=(x-4/3, x-4/3, z-2/3), and the vector coordinates x+z=2 are substituted by MG⊥AF and mg ⊥ cf.

So M(x, x, 2-x).

Point m is on EF, vector EM=λEF, and λ= 1/3 is obtained by substituting coordinates. So there is a point m on EF, which makes the triangular pyramid M-ACF a regular triangular pyramid.