On flexible polyhedral surfaces (Q492216)

A polyhedral 2-dimensional surface in Euclidean 3-space is said to be flexible if its spatial shape can be changed continuously due to changes of its dihedral angles only, i.\,e., if every face remains self-congruent during this deformation. The deformation is called a flex. The author constructs a closed orientable polyhedral surface of arbitrary genus that is embedded in Euclidean 3-space and admits a one-parameter flex under which all its handles change their shape. This surface admits no other flexes. The author also constructs a flexible closed nonorientable polyhedral surface of arbitrary genus such that all its handles and Möbius strips change their shape during the flex.