mat[a_]:={{Cos[a],-Sin[a]},{Sin[a],Cos[a]}}

vpol[n_]:=Table[{Cos[k*2Pi/n],Sin[k*2Pi/n]},{k,0,n}]

rettapar[P_,Q_]:=Expand[t*P+(1-t)*Q]

Manipulate[Graphics[{Red,Table[Line[Map[mat[k*2*Pi/m].(#+{x,0})&,a*vpol[n]]],{k,0,m-1}],Blue,Table[Circle[x*{Cos[k*2Pi/m],Sin[k*2Pi/m]},a/2],{k,0,m-1}]},ImageSize->150,PlotRange->{{-3,3},{-3,3}},Axes->True,AspectRatio->Automatic],{{n,5},2,64,1},{{m,5},2,64,1},{{a,0.4},0,2},{{x,1.5},0,3},ControlPlacement->Right]

Insert[{2,3},0,3]

Insert[{x,y},0,3]

Module[{k=1,m=3,x=1,a=.5,n=4},Map[mat[k*2*Pi/m].(#+{x,0})&,a*vpol[n]]]

prova={{-0.75`,1.299038105676658`},{-0.9330127018922193`,0.6160254037844386`},{-0.25`,0.4330127018922193`},{-0.0669872981077807`,1.1160254037844386`},{-0.75`,1.299038105676658`}}

prova[[2]]

Module[{k=1,m=3,x=1,a=.5,n=4,ls},ls=Map[Insert[(mat[k*2*Pi/m].(#+{x,0})),0,3]&,a*vpol[n]];
Table[rettapar[ls[[k]],ls[[k+1]]],{k,1,Length[ls]-1}]
]

Module[{ls,lseq,lspol},Manipulate[
ls=Map[Insert[(mat[k*2*Pi/m].(#+{x,0})),v,3]&,a*vpol[n]];
lseq=Table[rettapar[ls[[h]],ls[[h+1]]],{h,1,Length[ls]-1}];
lspol=Table[lseq,{k,0,m-1}];ParametricPlot3D[lspol,{t,0,1},{v,0,2},PlotRange->All,Mesh->None],{{n,5},2,64,1},{{m,5},2,64,1},{{a,0.4},0,2},{{x,1.5},0,3},ControlPlacement->Right]]

Module[{ls,lseq,lspol},Manipulate[
ls=Map[Insert[(mat[k*2*Pi/m].(#+{x,0})),0,3]&,a*vpol[n]];
lspol=Table[Polygon[ls],{k,0,m-1}];Graphics3D[lspol],{{n,5},2,64,1},{{m,5},2,64,1},{{a,0.4},0,2},{{x,1.5},0,3},ControlPlacement->Right]]

Module[{mr1=MeshRegion[vpol[4],Polygon[{1,2,3,4}]],
mr2=MeshRegion[.5vpol[4],Polygon[{1,2,3,4}]]},RegionDifference[mr1,mr2]]

Module[{mr1=Polygon[vpol[4]],
mr2=Disk[{0,0},.5]},DiscretizeRegion[RegionDifference[mr1,mr2]]]

Module[{ls,lspol,a=0.4,m=4,n=6,x=1},
ls=Map[Insert[(mat[k*2*Pi/m].(#+{x,0})),0,3]&,a*vpol[n]];
lspol=Table[Polygon[ls],{k,0,m-1}];Graphics3D[{lspol,Table[Sphere[x*{Cos[k*2Pi/m],Sin[k*2Pi/m],0},a/2],{k,0,m-1}]}]]

Module[{ls,lseq},Manipulate[
ls=Map[Insert[(mat[k*2*Pi/m].(#+{x,0})),v,3]&,a*vpol[n]];
lseq=Table[rettapar[ls[[h]],ls[[h+1]]],{h,1,Length[ls]-1}];
Show[{ParametricPlot3D[Table[lseq,{k,0,m-1}],{t,0,1},{v,0,2},PlotRange->All,Mesh->None],Graphics3D[{Table[Polygon[ls/.v->2],{k,0,m-1}],Table[Sphere[{x*Cos[k*2Pi/m],x*Sin[k*2Pi/m],2},a/2],{k,0,m-1}]}]}],{{n,5},2,64,1},{{m,5},2,64,1},{{a,0.4},0,2},{{x,1.5},0,3},ControlPlacement->Right]]

Module[{ls,lseq},Manipulate[
ls=Map[Insert[(mat[k*2*Pi/m].(#+{x,0})),v,3]&,a*vpol[n]];
lseq=Table[rettapar[ls[[h]],ls[[h+1]]],{h,1,Length[ls]-1}];
Show[{ParametricPlot3D[Table[lseq,{k,0,m-1}],{t,0,1},{v,0,2},PlotRange->All,Mesh->None],Graphics3D[Table[Polygon[ls/.v->2],{k,0,m-1}]]}],{{n,5},2,64,1},{{m,5},2,64,1},{{a,0.4},0,2},{{x,1.5},0,3},ControlPlacement->Right]]

Module[{ls,lseq,lspol},Manipulate[
ls=Map[Insert[(mat[k*2*Pi/m].(#+{x,0})),0,3]&,a*vpol[n]];
lspol=Table[Polygon[ls],{k,0,m-1}];Graphics3D[lspol],{{n,5},2,64,1},{{m,5},2,64,1},{{a,0.4},0,2},{{x,1.5},0,3},ControlPlacement->Right]]

Module[{ls},Manipulate[
ls=Map[Insert[(mat[k*2*Pi/m].(#+{x,0})),0,3]&,a*vpol[n]];ParametricPlot3D[Table[rettapar[ls[[k]],ls[[k+1]]],{k,1,Length[ls]-1}],{t,0,1},PlotRange->All],{{n,5},2,64,1},{{m,5},2,64,1},{{a,0.4},0,2},{{x,1.5},0,3},ControlPlacement->Right]]

Module[{k=1,m=3,x=1,a=.5,n=4,ls},ls=Map[Insert[(mat[k*2*Pi/m].(#+{x,0})),0,3]&,a*vpol[n]];
ParametricPlot3D[Table[rettapar[ls[[k]],ls[[k+1]]],{k,1,Length[ls]-1}],{t,0,1},PlotRange->All]
]

rettapar[{0,0},{1,2}]

rettapar[{0,0,0},{1,2,3}]

Manipulate[Graphics3D[{Red,Table[Line[Map[Insert[(mat[k*2*Pi/m].(#+{x,0})),0,3]&,a*vpol[n]]],{k,0,m-1}],Blue,Table[Sphere[x*{Cos[k*2Pi/m],Sin[k*2Pi/m],0},a/2],{k,0,m-1}]},ImageSize->150,PlotRange->{{-3,3},{-3,3},{0,3}},Axes->True,AspectRatio->Automatic],{{n,5},2,64,1},{{m,5},2,64,1},{{a,0.4},0,2},{{x,1.5},0,3},ControlPlacement->Right]