### Family I

Opposing vertices are used for the poles of spin. This creates three great circles which coincide with the octahedron's edges.

[Ref: ‘Geodesic Math And How To Use It’ p.53]

### Family II

Opposing mid-edge points are used for the poles of spin. This creates six great circles of which three appear on any face, coinciding with its medians.

[Ref: ‘Geodesic Math And How To Use It’ p.53]

### Family III

Opposing mid-face points are used for the poles of spin. This creates four great circles of which any face shows parts of three. This marks on the sphere the spherical equivalent of the cuboctahedron.

Note: the cuboctahedron is an Archimedean polyhedron that forms interior part common to the compound of a cube and an octahedron; it is also the dual of the rhombic dodecahedron.

[Refs: ‘Geodesic Math And How To Use It’ p.53; ‘Polyhderon Models’ p.25, by Magnus J. Wenninger; ‘Mathematical Models’ p. 102, by H.M. Cundy and A.P. Rollet]

### Families I & II

### Families I & III

### Families II & III

### Families I, II & III