Whether the surface of a polyhedron made of a flexible material such as paper can be flattened without cutting
or stretching is a problem that has been investigated. This problem has been solved for any 3-dimensional
convex polyhedron using moving (rolling) creases, and has been extended to higher dimensional polytopes.
We refer the set of facets for a polytope as surface. In this paper we focus on a 4-dimensional regular simplex
(a regular 5-cell) whose surface consists of five regular tetrahedra (facets). We provide a continuously folding
motion of its surface onto one facet such that the moving creases of this motion occupy one sixth of the surface
volume. Note that if we allow moving creases in the major part of the surface, such a continuous motion has been
given by the authors together with Abel et al., with creases whose total volume is four fifths of the surface's.
Hence, in this paper the ratio of rigid portions (not occupied by any moving creases) to the surface volume is
increased from one fifth to five sixths.
