In geometry, the 25 great circles of the spherical octahedron is an arrangement of 25

great circles In mathematics, a great circle or orthodrome is the circle, circular Intersection (geometry), intersection of a sphere and a Plane (geometry), plane incidence (geometry), passing through the sphere's centre (geometry), center point. Any Circula ...

in octahedral symmetry. 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 In geometry, the truncated cuboctahedron is an Archimedean solid, named by Kepler as a truncation of a cuboctahedron. It has 12 square faces, 8 regular hexagonal faces, 6 regular octagonal faces, 48 vertices, and 72 edges. Since each of its fac ...

. 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.

References

* Edward Popko, ''Divided Spheres: Geodesics and the Orderly Subdivision of the Sphere'', 2012, pp 21–22

Vector Equilibrium and its Transformation Pathways
Geodesic domes Polyhedra Circles {{geometry-stub

Construction

See also

References