Is this the only one?

Viewing a tetrahedron through opposite edges, we have, along with the 4 planes

From this, we see that the edge length is $\sqrt{10}$ , and the volume is

$\dfrac{1}{12}\sqrt{2} (\sqrt{10})^3 = 3.72678...$

First of all, you should put this regular tetrahedron into the cube FEGH-F'G'E'H' and satisfy that a coincides with E, B coincides with G, F coincides with' C, Dcoincides with H'. Then connect the midpoints Y,E'F' and X, H,H' of EF, which will form a plane. other planes can be made on the basis of it(moreover, by using vectors, we can prove that this scheme is unique.).After finishing the above work, the problem becomes easy.