変換F[{{a11_,a12_,a13_},{a21_,a22_,a23_},{a31_,a32_,a33_}}]:=
Module[{F1,F2,F3,F4,F5,F6,面,点,軸,枠1,枠2,枠3,F,A,f,FF},
F1={{0,0,0},{1,0,0},{1,0,5},{0,0,5},{0,0,0}};
F2={{1,0,5},{4,0,5},{4,0,4},{1,0,4},{1,0,5}};
F3={{1,0,2},{3,0,2},{3,0,3},{1,0,3},{1,0,2}};
F4=Map[ReplacePart[#,1,2]&,F1];
F5=Map[ReplacePart[#,1,2]&,F2];
F6=Map[ReplacePart[#,1,2]&,F3];
面[{{a1_,b1_},{a2_,b2_}}]:=
{{a1,0,b1},{a1,1,b1},{a2,1,b2},{a2,0,b2},{a1,0,b1}};
点={{0,5},{4,5},{4,4},{1,4},{1,3},{3,3},{3,2},{1,2},{1,0},{0,0},{0,5}};
F=Flatten[{{F1,F2,F3,F4,F5,F6},
Table[面[Take[Drop[点,k],2]],{k,0,9}]},1];
A={{a11,a12,a13},{a21,a22,a23},{a31,a32,a33}};
f[x_]:=A.x;
FF=Table[Map[f,F[[k]]],{k,1,16}];
軸={Line[{{-6,0,0},{6,0,0}}],
Line[{{0,-6,0},{0,6,0}}],
Line[{{0,0,-6},{0,0,6}}]};
枠1=Line[{{6,0,-6},{6,0,6},{-6,0,6},{-6,0,-6},{6,0,-6}}];
枠2=Line[{{0,-6,6},{0,-6,-6},{0,6,-6},{0,6,6},{0,-6,6}}];
枠3=Line[{{-6,6,0},{-6,-6,0},{6,-6,0},{6,6,0},{-6,6,0}}];
Show[Graphics3D[{Glow[Red],Map[Polygon,FF],軸,枠1,枠2,枠3}],
Axes->True,AxesOrigin-> {0,0,0},AxesStyle-> Directive[Blue],AxesLabel->{"(Subscript[x, 1])","(Subscript[x, 2])","(Subscript[x, 3])"},
PlotRange->All]]

変換F[IdentityMatrix[3]]

変換F[{{1,-1,0},{0,1,0},{0,0, 1}}]

回転[a_,b_,c_]:={{Cos[c],-Sin[c],0},{Sin[c],Cos[c],0},{0,0,1}}.
{{1,0,0},{0,Cos[b],-Sin[b]},{0,Sin[b],Cos[b]}}.
{{Cos[a],-Sin[a],0},{Sin[a],Cos[a],0},{0,0,1}}

Manipulate[変換F[回転[0,π t,0]],{t,0,2,0.1}]