English: Unfolding of six faces of a platonic dodecahedron, with notations and equalities. KLMNP  is the smallest polygon containing the six unfolded faces. RSUVW is the central face. The side length of all the faces is RS or a, their diagonal length is d or  φ a,  where φ denotes the golden ratio. G is the common center of KLMNP and RSUVW, which are two convex regular pentagons. The symmetry with respect to G transforms KLMNP into ABCEF. So ALCNFKBMEP is a stellated regular decagon with the same center. Its drawing reveals that of a convex regular decagon with the same center. This convex decagon in thick brown line is the outline of the sheet when folded. We can imagine an animated view of the folding, where RSUVW is fixed, and where a movable vertex of the sheet is depicted by K, which moves on the perpendicular bisector of [UV ]. On this straight line H is a vertex of the decagon, it is the point of arrival of K. On the paths of the images of two movable vertices of the sheet, two arrows are pointing to another point of arrival, another vertex of the decagon, the intersection of (CL ), (FK ) and (EV ).
In this image or in this other one, the outline of the dodecahedron is the same in the top view. The distance between two opposite sides of the outline is the real distance between two opposite edges of the solid, equal to  MN  or  φ d.