Consider the perspective view of a known equilateral triangle. It is not hard to see that the same perspective measurement can be obtained from different configurations. In other words, if such a measurement were to be used to determine the position of the camera relative to the triangle there would be ambiguities. When the vertices of the triangle are not distinguishable, the symmetry of the equilateral triangle (120° rotations about its center and reflections through an altitude) produces six configurations consistent with a single perspective view. Choosing one of these is equivalent to choosing a correspondence between imaged and actual vertices. But even for a given correspondence, there can be as many as four distinct solutions. Thus, for an equilateral triangle whose vertices are indistinguishable, there can be as many as 24 configurations that give the same measurement.
William J. Wolfe,
Katheryn F. Jones,
"Camera Calibration Using The Perspective View Of A Triangle", Proc. SPIE 0730, Automated Inspection and Measurement, (18 May 1987); doi: 10.1117/12.937856; https://doi.org/10.1117/12.937856