Take two copies of a hyperbolic triangle whose interior angles are integer submultiples of pi, and identify these two triangles together in the natural way along their boundaries. The result is called a hyperbolic turnover, and is a specific example of a hyperbolic 2-orbifold. In this talk, we will see that mapping a turnover by an immersion (which is not an embedding) into a hyperbolic 3-orbifold places strong restrictions on (among other things) the volume of the 3-orbifold.

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