# 25 great circles of the spherical octahedron

From HandWiki

In geometry, the **25 great circles of the spherical octahedron** is an arrangement of 25 great circles in octahedral symmetry.^{[1]} It was first identified by Buckminster Fuller and is used in construction of geodesic domes.

## Construction

The 25 great circles can be seen in 3 sets: 12, 9, and 4, each representing edges of a polyhedron projected onto a sphere. Nine great circles represent the edges of a disdyakis dodecahedron, the dual of a truncated cuboctahedron. Four more great circles represent the edges of a cuboctahedron, and the last twelve great circles connect edge-centers of the octahedron to centers of other triangles.

## See also

## References

- Edward Popko,
*Divided Spheres: Geodesics and the Orderly Subdivision of the Sphere*, 2012, pp 21–22. [1] - Vector Equilibrium and its Transformation Pathways

Original source: https://en.wikipedia.org/wiki/25 great circles of the spherical octahedron.
Read more |