# trisection

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## trisection

[trī′sek·shən]
(mathematics)
The problem of dividing an angle into three equal parts, which is impossible to do with straight edge and compass alone.
References in periodicals archive ?
g](n) be the set of unicellular maps of genus g with n edges, and a distinguished trisection.
1](n) of unicellular maps of genus 1 with n edges and a distinguished trisection is in bijection with the set [U.
Let M be a unicellular map of genus 2, and [tau] be a trisection of M.
2], [tau]) satisfying Equation 6, and then to apply the mapping [PSI] to retrieve a map of genus 2 with a marked trisection of type II.
2](n) of unicellular maps of genus 2 with one marked trisection is in bijection with the set [U.
2]q+1 together, via the mapping [PHI], in order to obtain a new map Mi of genus p + I with a distinguished trisection [tau] of type I.
2]q-2i, [tau]) be the triple consisting of the last two vertices which have not been used until now, and the trisection [tau].
We let A(M, v*) := (Mq, [tau]) be the map with a distinguished trisection obtained at the end of this procedure.
In other words, all unicellular maps of genus g with a distinguished trisection can be obtained in a canonical way by starting with a map of lower genus with an odd number of distinguished vertices, and then applying once the mapping and a certain number of times the mapping 'J/.
Given a map with a marked trisection (M, [tau]), the converse application consists in slicing recursively the trisection [tau] while it is of type II, then slicing once the obtained trisection of type I, and remembering all the vertices resulting from the successive slicings.

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