Exespheres::usage="Given the vertices of a tetrahedron, the excenter abd the exradius of each exinscribed sphere are obtained.You just have to provide the vertices of a tetrahedron in the command below, evaluate notebook.Reference: Personal.";
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NotableSphere[tet={{ax_,ay_,az_},{bx_,by_,bz_},{cx_,cy_,cz_},{dx_,dy_,dz_}}]:=Module[{},prueba=Det[{{1,ax,ay,az},{1,bx,by,bz},{1,cx,cy,cz},{1,dx,dy,dz}}];If[prueba==0,Print[PasteButton["It's not a tetrahedron"]],ρ=ResourceFunction["Exspheres"][tet];s=Grid[{{{c1,r1},{c2,r2},{c3,r3},{c3,r4}},{{N[ρ[[1,1]]],N[ρ[[1,2]]]},{N[ρ[[2,1]]],N[ρ[[2,2]]]},{N[ρ[[3,1]]],N[ρ[[3,2]]]},{N[ρ[[4,1]]],N[ρ[[4,2]]]}}},FrameAll];Print[s];Show[{Graphics3D[{Tube[#]&/@Subsets[tet,{2}],Green,Opacity[0.2],Polygon/@Subsets[tet,{3}]}],Graphics3D[{Opacity[0.1],Green,InfinitePlane/@Subsets[tet,{3}]}],Graphics3D[{Black,Ball[ρ[[1,1]],0.04],Ball[ρ[[2,1]],0.04],Ball[ρ[[3,1]],0.04],Ball[ρ[[4,1]],0.04]}],Graphics3D[{Opacity[0.6],ρ[[1]],ρ[[2]],ρ[[3]],ρ[[4]]}]},AxesLabel->(Style[#,15,Blue]&/@{"X","Y","Z"}),AxesOrigin{0,0,0},AxesTrue,BoxedFalse,BoxRatiosAutomatic,PlotRangeAll]]]
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NotableSpheretet=,0,-,-,0,-,0,,0,0,
2
2
6
6
2
2
6
6
2
,-6
6
6
3
{c1,r1} | {c2,r2} | {c3,r3} | {c3,r4} |
{{0.,0.598758,-1.00701},0.598758} | {{0.,-0.529408,0.12116},0.529408} | {{0.825875,0.656339,0.248091},0.656339} | {{-0.825875,0.656339,0.248091},0.656339} |
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