Pair of pants
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In mathematics, a pair of pants is a simple two-dimensional surface resembling a pair of pants. In hyperbolic geometry, pairs of pants are sewn together, leg to leg, or leg to waist, to create Riemann surfaces of arbitrary genus. Because the "legs" can be twisted before being sewn together, there is a large amount of freedom in how the pants can be assembled. This ambiguity is then the moduli space of the Riemann surface.
Formally, a pair of pants consists of two hexagonal fundamental polygons stitched together at every other side. Topologically, a pair of pants is the two-sphere S2 with three points removed.
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