= Cone point of an orbifold
{title2=$2\pi/m$}
A cone point of an oriented two-dimensional <orbifold> is a point with a chart modeled on a disk modulo a nontrivial finite cyclic rotation group. For a group of order $m$, its local quotient metric has total angle $2\pi/m$, and its <stabilizer> is cyclic of order $m$.
For example, identifying the edges of a planar sector of angle $2\pi/3$ gives the local order-three model. The underlying quotient neighborhood is homeomorphic to a disk, so the cone order is not detectable from topology alone. A point with order one is an ordinary nonsingular point.
A cone point is distinct from a mirror boundary point, whose local group acts by a reflection. It also differs from a general metric cone singularity: an orbifold cone angle must be of the form $2\pi/m$ with positive integer $m$. A <teardrop orbifold> has exactly one such exceptional point on an underlying sphere.
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