# Curtis Palmer

How does one represent an icosahedron? (0,±φ, ±1), (±1, 0, ±φ), (±φ,
±1, 0) works for some. In this work,

In-spheres, Inter-spheres and Circum-spheres with origins on the
vertices, mid-edges and face centres of an icosahedron define an
arbitrary domain of competing forces acting upon an origin. Close
attention to the orientation of these spheres results in pleasing
patterns when viewed along axes of icosahedral symmetry.

Spheres in Rhinoceros 3D wire frame mode are represented as semi-circles, like the letter 'C'. Spheres of radii 1, 0.851=(cos(arctan(φ⁻¹))) and 0.795=(cos(arctan(2φ⁻²))) are positioned at the vertices, mid-faces and mid-edges of the icosahedron. They are all tangent to the origin. Five spheres at each vertex in a polar array with 72 degree rotation, three spheres at each face center with 120 degree rotation, and one sphere at each mid-edge of the icosahedron. These are plotted aligned to the axes of symmetry.