Wolfram Demonstrations Project

12,000+ Open Interactive Demonstrations
Powered by Notebook Technology »

Vélez-Jahn's Möbius Toroidal Polyhedron

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

In 1968, Gonzalo Vélez-Jahn (UCV, Caracas, Venezuela) discovered three-dimensional bodies with Möbius-like characteristics, later described by Martin Gardner as prismatic rings that became toroidal polyhedrons. The face trajectories show that this set of cubes behaves as if it were a one-sided Möbius strip. This Demonstration lets you switch between the 10- and 22-cube versions, showing an animated trajectory on the faces.

[more]

This Demonstration displays the Möbius-like polyhedra as an assembly of blue cubes, the path around the single side of the figure as an orange tube, and a particular step along the path as a red sphere.

[less]

Contributed by: Gonzalo Vélez-Jahn, Luis Vélez, Roger Bagula, and Robert Dickau (March 2016)
Open content licensed under CC BY-NC-SA

Snapshots

Details

This code was developed as a cooperative effort by Robert Dickau and Roger Bagula at the request of Luis Vélez, the son of Gonzalo Vélez-Jahn.

References

[1] M. Gardner, "Twisted Prismatic Rings," Fractal Music, Hypercards and More...: Mathematical Recreations from Scientific American Magazine, New York: W. H. Freeman, 1991.

[2] G. Vélez-Jahn, "Diseñando Lo Futuro: Edificaciones Hibridas," Primer Seminario de Realidad Virtual, Concepción: Universidad del Bío-Bío, 1995.

[3] G. Vélez-Jahn, "Professor Gonzalo Velez Jahn," Moebius 3D Wiki. (Mar 18, 2016) moebius-3d.wikia.com/wiki/Professor_Gonzalo_Velez _Jahn.

[4] R. G. Alvarado, "Projected Space: Characterizing the 'Cybrid Architecture'," from Proceedings of the 5th Iberoamerican Congress of Digital Graphics, 2001 pp. 285–287.

[5] G. Vélez-Jahn, "Mobius Strip: Research for 3D Aplication [i.e. Application] (Space ; no. 2)," 1979. www.amazon.com/Mobius-strip-Research-aplication-application/dp/B0006EE65A.

Embed Code

Take advantage of the Wolfram Notebook Emebedder for the recommended user experience.

Related Demonstrations More by Author
Browse all topics
Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send