I have answered this question before, but your question is wrong. If all six sides are A, the tetrahedron is fixed and has no maximum volume; The solid should be "all five edges are one"

The original tetrahedron can be regarded as a spatial body in which two equilateral triangles rotate around a common edge. It can be seen that the volume of tetrahedron should be maximized, that is, the height of tetrahedron should be maximized, and the volume will be maximized if and only if the faces of two equilateral triangles are perpendicular.

At this point, the area of the equilateral triangle at the bottom is S=√3/4a? , height H=√3/2a,

∴V= 1/3×√3/4a？ ×√3/2a= 1/8a？