C (on Windows), 297 295295 294 bytes
#import<windows.h>
#define P(x,y,s)C.X=X+x;C.Y=Y+y;SetConsoleCursorPosition(GetStdHandle(-11),C);puts(s);
COORD C;X,Y,R,r,c;t(){P(2,-2,"/\\")P(1,-1,"//\\\\")P(0,0,"///\\\\\\")P(2,1,"||")P(2,2,"||")}f(n){for(c=R=r=1;c<n;c+=++R);for(;r;r++)for(c=0;++c<r+1;){X=(R-r-2)*4+c*8;Y=r*2;t();r=r=--n?r:-1;1);}}
Similar to my C++ answer, but I posted this because it's somewhat shorter in C.