Norden's fourth Pyramid and the Orion Correlation theory (no replies)

The Danish naval Captain Frederic Louis Norden described a fourth, main, pyramid in his travel logs (published 1755). His (highly detailed) sketches clearly show it as part of the main pyramidical "constellation." It was described as buildt with far darker stone than the other three, but the smallest in stature. Contemporary sources place the date of it's destruction to around 1758 (the materials were allegedly used to rebuild parts of Kairo after an earthquake).

What I am curious about is how this fourth pyramid would fit within Robert Bauval's 'Orion Correlation theory.'
There are many astronomical phenomena within the proximity of this constellation the Ancient Egyptians could have taken interest in. There is (for example) a black hole in the Orion Nebula; discovered by a team of astrophysicists in 2012.

The stars and phenomenas surrounding Orion's Belt are not necessarily configured exactly as it was in the Era the pyramids reflect, and Orion's belt's placement in the night

sky sertainly isn't.

So what cosmic object could this fourth pyramid represent, within proximity of the stars of Orion's Belt? If we (at least for the sake of speculation) accept it's existence.

PS' Norden's book is in public domain and digital copies (and articles about it) are easy to find.