# Vélez-Jahn's Möbius Toroidal Polyhedron

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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.

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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.

## Permanent Citation

"Vélez-Jahn's Möbius Toroidal Polyhedron"

http://demonstrations.wolfram.com/VelezJahnsMoebiusToroidalPolyhedron/

Wolfram Demonstrations Project

Published: March 21 2016