Do[Clear[a,h];v = 6;(* number of turns*)
p0 = {1,0,0}; p1 = {Cos[a],Sin[a],h};
pn = {Cos[n*a], Sin[n*a],n*h};
{h,a} = {h,a}/.FindRoot[{(p0-p1).(p0-p1)==(p0-pn).(p0-pn),
(p0-p1).(p0-p1)==(p1-pn).(p1-pn)},{h,.2},{a,2*Pi/n}];
pts = Table[Chop[{Cos[a*j],Sin[a*j],j*h}],{j,0,v*n}];
tri[j_] := {pts[[j]],pts[[j+1]],pts[[j+n]],pts[[j]]};
lines = Table[tri[j],{j,1,(v-1)*n}];
facelist = Map[Line,lines];

gra = {Graphics3D[{Thickness[.002],facelist}]};

viewpt = 100{1000, 300, 350};
Show[gra, ViewPoint -> viewpt,  PlotRange -> All,
Lighting -> False, Boxed -> False ],{n,3,5}];