My Transformable Structures Based on the Möbius Strip

Leuncrrclo, Vol. 8, pp. 148-149. Pergamon Press 1975. Printed in Great Britain MY TRANSFORMABLE STRUCTURES BASED ON THE MOBIUS STRIP Sebastian (Enrique Carbajal G . ) * In 1966 I made a number of small sculptures of folded paper and cardboard. These objects, which I call desplegables (Spanish for ‘unfolding’), were responsible for directing my attention to the branch of geometry called topology [I, 21. I read about topological spaces with the hope of finding something to serve me in my art. In this quest I became acquainted with and much fascinated by the Mobius str$. It can be described as follows: A long rectangle (e.g. a strip of paper, 2 x 30 cm.) is held fixed at one end and turned through 180” at the other end. The two ends are then joined yielding a one-sided surface [I]. On such a surface, if one places one’s finger at any point on it and then moves the finger along the strip, the finger will return to the starting point after traversing the surface on both sides of the untwisted strip. My first object, a folding sculpture, (1967) utilizing the idea of twisting and joining in a ring (40 cm. diameter) was made from a paper strip containing creases delineating a chain of equilateral triangles. This strip was given three twists (540”),instead of just one (180”), as in the Mobius strip. The resulting one-sided surface can be transformed, by folding, into five different 3dimensional forms and one 2-dimensional shape that has a hexagonal perimeter; hence the name that I gave to this type of construction is ‘Hexaflexagono ’. Art objects made of elements that can be rearranged by a viewer are called transformables [3] and paintings and sculptures of this kind have been devised by numerous artists in recent years [4]. 1 then wished to see whether other objects with flexion characteristics similar to those of a ‘Hexaflexagono ’ could be made and whether other polygons might be formed. I found that they could and T devised a procedure in which the folding and twisting were varied. Although the formation of a Mobius strip represents one stage in their fabrication , the topological property of the Mobius strip is not preserved in the final folded objects. The ‘Tetraflexagono’, which 1 constructed in this way, can be arranged into a 2-dimensional square and into other forms including that of a cube. I have prepared a printed edition of a ‘Tetraflexagono’, with colored circular and linear stripes on the * Artist living at Cda. Protasio Tagle 33, Mexico City, 18 D.F., Mexico. (Received 19 Nov. 1973.) I48 surface of the elements to add interest to the various forms into which it can be transformed My earlier studies of crystallography [6] and my experience with the Mobius strip influenced the design of my next object. I made of paper a ring of tetrahedrons that can turn on its central axis. 1then devised a scheme (called ‘structural strategy’ PI. Fig. 1. ‘Estrrrctrrra Articirlada’, trairsfurnwble scrrlptrrre ( o m uf itspussiblefortiis), ivuud, Iacyirer, 30 x 30 x 30 cni. (I 970). Fig. 2. ‘Ciibu Hescrcdirico’, trutisfurrirahlc, scrilptrrre (utw of its possible fortiis), cardbuord, acrylic poitit, 30 x 30 x 30 cm. (1970). (Cf. Figs. 3 and 4.) Sebasticin (Enrique Carbajal G.) 149 by Jiirgen Claus [7] for cutting, folding and twisting a chain that permits the making of transformables with geometrical and architectonic forms (Figs. 1 and 2) [8]. Figs. 2 and 3 show two of the transformations obtained with the object ‘Cubo Hexagonico ’. Fig. 4 shows the final layout for ‘Cubo Hexagonico ’, which represents the first step in making one of my paper transformables. To arrive at a layout that leads to a feasible 3-dimensional transformable is quite complicated and requires considerable experience. My ideas about architectonic structures were influenced by reading a book on architecture by Michel Ragon [9] and by the sculptures and architectural work of Mathias Goeritz [lo, 111. I am much interested in the housing of people and, in particular, in the need to adapt housing to radically different ways of living. Thus, I have begun to investigate habitable underground, underwater and Fig. 4. Layoiit for the transformable sciilptiire...