Tensegrity Analysis

Our goal is to demonstrate a static analysis of the tensegrity structure given by

IcosahedronVertices = PolyhedronData["Icosahedron"][[1,1]];

Show[Graphics3D[Table[Tooltip[Sphere[IcosahedronVertices[[i]],0.05],ToString[i]],{i,1,12}]],PolyhedronData["Icosahedron"]]

Struts = {{2,3},{4,1},{11,12},{9,10},{5,7},{6,8}};

StrutGraphics = Graphics3D[Cylinder[{IcosahedronVertices[[#[[1]]]],IcosahedronVertices[[#[[2]]]]},0.03]&/@Struts]

Show[StrutGraphics,Graphics3D[Table[Tooltip[Sphere[IcosahedronVertices[[i]],0.05],ToString[i]],{i,1,12}]]]

Cables = {{2,11},{2,12},{11,4},{4,12},{2,7},{2,8},{4,5},{4,6},{3,9},{3,10},{9,1},{10,1},{3,7},{3,8},{1,5},{1,6},{11,7},{11,5},{7,9},{5,9},{12,6},{12,8},{6,10},{8,10}};

CableGraphics = Graphics3D[Cylinder[{IcosahedronVertices[[#[[1]]]],IcosahedronVertices[[#[[2]]]]},0.01]&/@Cables]

Show[StrutGraphics,CableGraphics,Graphics3D[Table[Tooltip[Sphere[IcosahedronVertices[[i]],0.05],ToString[i]],{i,1,12}]]]