# Möbius Triangles

Requires a Wolfram Notebook System

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

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

This Demonstration shows Möbius triangles on a sphere. Möbius triangles are congruent spherical triangles that completely cover a sphere without overlap. The angles of these triangles are , , and , where , , and are in the set . Such a Möbius triangle is denoted by . There is an infinite family of dihedral Möbius triangles, and three triangles , , and that correspond to the tetrahedral, octahedral, and icosahedral symmetry groups, respectively.

Contributed by: Izidor Hafner (October 2014)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The numbers must satisfy the inequality [1, p. 157]. The definition of Möbius triangle was taken from [2, p.189].

References

[1] W. W. R. Ball and H. S. M. Coxeter, *Mathematical Recreations and Essays*, 13th ed., New York: Dover, 1987 pp. 133, 160.

[2] R. E. Maeder, *The Mathematica Programmer II*, San Diego: Academic Press, 1996.

## Permanent Citation