Main points of research:
  • 'Rectangularization' of models of the Möbius Strip. Properties and description of the logical process which led to the attainment of the first rectangular version of a Möbius strip. Speculation on potential situations, contributions and benefits. Discovery date: 1965.

  • Exploration of variations and characteristics of the new rectangular Möbius Strip discovered, as well as of the family of shapes that derive from it. Re-evaluation of the edge of the Strip, ignored by previous topological modeling. Discovery of 3D bodies posessing 3D Möbian characteristics in 1968. First date of publication of results: April 1974 (Revista "PUNTO", FAU-UCV) . First references to Professor Velez Jahn's work with rectangular 3D Möbius bodies by Martin Gardner in Aug. 1978 ("Mathematical Games", Scientific American) where he coined the name "Toroidal Polyhedra" (TP)...
  • External exploration of Toroidal Polyhedra (TP). Identification of its topological generation, grouping and typology. Behavior of walls and surface continuity.
  • Transparency in the perception of the interior of TP.
  • Internal Exploration of TP assuming an architectural behavior.
  • Continuity: study of internal circulation. Types of continuity identified. Potential applications.Transparency of walls. Sculptural and Use of 3D color possibilities.
  • Internal typology of TP regarding tunnel continuity: a) Four independed non-connected tunnels. b) Two independing non-connected tunnels one single continuous tunnel. The TP corresponding to this second group correspond to the 3D Möbius TP. c) The single tunneled TP, which is one of the most important discoveries of this research because its continuity escapes referred TP Möbius classification, seeming to belong to an even simpler origin that the rectangular Möbius strip but which proves impossible to be reached directly through our third dimension.
    Screen shot 2011-09-27 at 27Sep10.34.33 PM-1

    Moebius 3D

  • Typologies derived from the three basic groups previously identified. On the basis of these earlier classifications, each of the three groups can be broken down into further subgroups depending on the different arrangements for a similar number of components.
  • Future applications of Toroidal Polyhedra in 3D Digital Space via Internet. And of the possibility of exploring continuity effects upon real visitors (represented by avatars) as they walk, drive or levitate within the interior space of sculptural or even architectural space where they join a crowd of visitors at different stages of the process of exploring and appraising inner TP spaces. Imagine the potencial that Second Life would offer to this initiative...!
  • Secondlife-postcard

    Moebius 3D in Second Life.

    To be added: conclusions and references consulted while developing this work.

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