25 great circles of the spherical octahedron 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. ConstructionThe 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 alsoReferences
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