It is known that a general quintic equation cannot be solved by an ordinary origami construction. Alperin and Lang showed that three simultaneous folds leads to a solution of the general quintic equation. In this paper we improve their result and show that two simultaneous folds are sufficient to solve the general quintic equation.

No abstract

We study two operations on 3-dimensional small covers called connected sum and surgery. These operations correspond to combinatorial operations on ‫ޚ(‬ 2 ) 3 -colored simple convex polytopes. Then we show that each 3-dimensional small cover can be constructed from T 3 , ‫ޒ‬ P 3 and S 1 × ‫ޒ‬ P 2 with two different ‫ޚ(‬ 2 ) 3 -actions by using these operations. This is a generalization of the results of Izmest'ev and Nishimura, and an improvement of the results of Kuroki and Lü and Yu.

No abstract