I want to find the moment of inertia of the following symbolic octahedron:

Octahedron[{\[Theta], \[CurlyPhi]}, \[ScriptL]]

I can find the moment of inertia of a symbolic edge length:

MomentOfInertia[Octahedron[\[ScriptL]]] // MatrixForm

Output:

{{\[ScriptL]^5/(15 Sqrt[2]), 0, 0}, {0, \[ScriptL]^5/(15 Sqrt[2]), 
  0}, {0, 0, \[ScriptL]^5/(15 Sqrt[2])}}

I can't get MomentOfInertia to evaluate with a symbolic edge and an angle:

MomentOfInertia[Octahedron[{1, 2}, l], 
 Assumptions -> {\[ScriptL] > 0}]

I would like to be able to evaluate the following:

MomentOfInertia[Octahedron[{\[Theta], \[CurlyPhi]}, \[ScriptL]]]

Is there a way to find a rotated octahedron's symbolic moment of inertia? I realize this might not be possible. As an example of a concrete case, if the first angle is 1 and the second angle is 2 and the edge length is 3 we have:

MomentOfInertia[Octahedron[{1, 2}, 3]]

The output is a tensor:

{{81/20 (Cos[1]^2 + Cos[2]^2 + Sin[1]^2 + Cos[1]^2 Sin[2]^2 + 
     Sin[1]^2 Sin[2]^2) (Sqrt[2] Cos[1]^2 Cos[2]^2 + 
     Sqrt[2] Cos[2]^2 Sin[1]^2 + Sqrt[2] Cos[1]^2 Sin[2]^2 + 
     Sqrt[2] Sin[1]^2 Sin[2]^2), 0, 
  81/20 (-Cos[2] Sin[2] + Cos[1]^2 Cos[2] Sin[2] + 
     Cos[2] Sin[1]^2 Sin[2]) (Sqrt[2] Cos[1]^2 Cos[2]^2 + 
     Sqrt[2] Cos[2]^2 Sin[1]^2 + Sqrt[2] Cos[1]^2 Sin[2]^2 + 
     Sqrt[2] Sin[1]^2 Sin[2]^2)}, {0, 
  81/20 (1 + Cos[1]^2 + Sin[1]^2) (Sqrt[2] Cos[1]^2 + 
     Sqrt[2] Sin[1]^2) (Cos[2]^2 + Sin[2]^2)^2, 
  0}, {81/20 (-Cos[2] Sin[2] + Cos[1]^2 Cos[2] Sin[2] + 
     Cos[2] Sin[1]^2 Sin[2]) (Sqrt[2] Cos[1]^2 Cos[2]^2 + 
     Sqrt[2] Cos[2]^2 Sin[1]^2 + Sqrt[2] Cos[1]^2 Sin[2]^2 + 
     Sqrt[2] Sin[1]^2 Sin[2]^2), 0, 
  81/20 (Cos[1]^2 + Cos[1]^2 Cos[2]^2 + Sin[1]^2 + Cos[2]^2 Sin[1]^2 +
      Sin[2]^2) (Sqrt[2] Cos[1]^2 Cos[2]^2 + 
     Sqrt[2] Cos[2]^2 Sin[1]^2 + Sqrt[2] Cos[1]^2 Sin[2]^2 + 
     Sqrt[2] Sin[1]^2 Sin[2]^2)}}