= Untwisted band
{title2=$S^1\times[-1,1]$}
An untwisted band is the <topological surface> obtained from a rectangle by identifying $(0,v)$ with $(1,v)$. It is the <Cartesian product> of a <circle> and a <closed interval>, and is <homeomorphic> to a closed <annulus>. A finite portion of the lateral surface of a <circular cylinder> realizes it in three-dimensional space. Its two <boundary> circles are $S^1\times\{-1\}$ and $S^1\times\{1\}$, and the matching seam directions make it an <orientable surface>. The <Möbius band> changes just one identification sign and loses both this two-component boundary and its <orientability>.
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