Planetary nebulae (PNe) have diverse morphological shapes, including point-symmetric and multipolar structures. Many PNe also have complicated internal structures such as tori, lobes, knots, and ansae. A complete accounting of all the morphological structures through physical models is difficult. A first step toward such an understanding is to derive the true three-dimensional structure of the nebulae. In this paper, we show that a multipolar nebula with three pairs of lobes can explain many such features, if orientation and sensitivity effects are taken into account. Using only six parameters—the inclination and position angles of each pair—we are able to simulate the observed images of 20 PNe with complex structures. We suggest that multipolar structure is an intrinsic structure of PNe and the statistics of multipolar PNe have been severely underestimated in the past.
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