# Sphere in Mirrored Spheroid

A **spheroid** is an ellipsoid with an axis of rotational symmetry. This image created by John Valentine shows a sphere inside a mirrored spheroid, reflected almost endlessly.

A **spheroid** is an ellipsoid with an axis of rotational symmetry. This image created by John Valentine shows a sphere inside a mirrored spheroid, reflected almost endlessly.

A **Schwarz triangle** is a spherical triangle that can be used to generate a tiling of a branched covering of the sphere by repeatedly reflecting this triangle across its edges. Sometimes we get an actual tiling of the sphere, but in general we get a branched covering, because the same point can lie in the interior of several triangles, and there may be branch points at the corners of the triangles.

Notices of the AMS · Bulletin of the AMS

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