= Convex regular spherical polygon
{title2=$\frac{n-2}{n}\pi<\alpha<\pi$}
A nondegenerate convex regular spherical $n$-gon contained in an <open hemisphere> has equal interior angles $\alpha$ in the displayed interval. The <spherical excess formula> gives area $n\alpha-(n-2)\pi>0$. Conversely, put equally spaced vertices at colatitude $t\in(0,\pi/2)$ around a pole. Dividing each central triangle in half gives $\cot(\alpha/2)=\cos t\tan(\pi/n)$ by the <spherical law of cosines>. As $t$ increases, the angle ranges continuously from the Euclidean limiting angle to $\pi$.
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