Developing a tetramonohedron with minimum cut length

In this paper, we investigate the way of unfolding a given tetramonohedron, which is a tetrahedron that consists of four congruent triangles. Our aim is finding a way that achieves the minimum cut length to develop it. We first show the rigorous way to unfold any given tetramonohedron with minimum cut length. Next, we focus on a family of tetramonohedra that consist of four congruent isosceles triangles. For this family, we apply our result and investigate their behavior. (C) 2022 Elsevier B.V. All rights reserved.