Here the familiar 22 degree radius halo takes on a new guise. Small randomly oriented crystals on the frozen surface refract the sun's rays in an identical way to those in the sky.
To an otherwise very unbiased eye or camera the halo is circular like its welkin counterpart. However, the path of the glinting crystals across the ice is a section through a cone, a hyperbola.
The glinting crystals - in the sky or on the ground - lie on or outside the surface of a cone extending from the eye and with a half angle of 22 degrees. For ground halos, the path of glints along the ground is where it intersects this cone.
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