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This article analyses geometric constructions by origami when up to $n$simultaneous folds may be done at each step. It shows that any arbitrary anglecan be $m$-sected if the largest prime factor of $m$ is $p\le n+2$. Also, theregular $m$-gon can be constructed if the largest prime factor of $\phi(m)$ is$q\le n+2$, where $\phi$ is Euler's totient function.

Division of an angle into equal parts and construction of regular polygons by multi-fold origami