Pensieve Header: An embedded Mobius band whose boundary is a rectangle; continued pensieve://2011-12/.

dt=2Pi/12;
s=2Pi;
Graphics3D[
Table[
{
Polygon[{
{t/s,0,0},{t/s,Cos[t], Sin[t]},{(t+dt)/s,Cos[t+dt],Sin[t+dt]},{(t+dt)/s,0,0}
}],
Polygon[{
{t/s,Cos[t], Sin[t]},{(t+dt)/s,Cos[t+dt],Sin[t+dt]}, {(2Pi+t+dt)/s,Cos[t+dt],Sin[t+dt]}, {(2Pi+t)/s,Cos[t], Sin[t]}
}],
Polygon[{
{(2Pi+t)/s,0,0},{(2Pi+t)/s,Cos[t], Sin[t]},{(2Pi+t+dt)/s,Cos[t+dt],Sin[t+dt]},{(2Pi+t+dt)/s,0,0}
}]
},
{t, 0, 2Pi-dt, dt}
]
]

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