The figure shows how Khufu might have imagined he would spend his eternity, using his pyramid Akhet Khufu, the Horizon of Khufu, as his "jumping-off" base.
The ancient Egyptians had a problem — they wished to project the King's ka to the stars, and to retrieve him, but they did not know how. The Pyramid Texts have a number of suggestions: rising on smoke, going up with thunderclouds, climbing a rope to the Great Hitching Post (celestial north pole, the star Thuban at the time), and others. The solution for Khufu's Pyramid was to use daily prayer and offerings by a dedicated priesthood as a the power source to project the King's ka… so, the Great Pyramid complex became a psychic machine!
There were several places the King's ka would visit, and these are all catered for in the design of Akhet Khufu. They also seem to be arranged so that he could travel by day or night. By day, the King would spend his time in the so-called Queen's Chamber, more likely a serdab for a missing ka statue of the king which would have fitted into the niche built into the East wall of the chamber. From this serdab, his ka could roam either north or south, as shown in the figure, so that he could look after his people and maintain Ma'at. Whether he envisaged travel over land and river, or instead over a figurative map of the land and river on top of the Mound of Creation, is moot. There were, after all, several boats buried near the pyramid which he might be able to magically reassemble and use…or not.
By night, he could travel from the King's Chamber to the Southern Netherworld, which was presumed to be in the direction of Al Nitak, the leftmost star in Orion's Belt, which culminated at 45˚, matching the slope of the shaft KC(S). Here the King would engage with other gods of the heavens to negotiate a good Inundation for his people of Egypt. Or, the King could travel to the Northern Netherworld, where his stellar palace awaited him, and where he would become an "akh", a shining one: KC(N) was aimed at the Great Hitching Post.
It seems likely that the abandoned subterranean chamber had been intended, originally, to allow the King to commune with the Netherworld deep underground - another entrance to that fabulous place, as it were. To compensate for this loss, it seems that the redundant, so-called Relieving Chambers were more likely to form a pit burial from the hidden upper surface of the Mound of Creation, with the King's Chamber and sarcophagus at the bottom of the pit. (Khufu would be aware that King Djoser, whose architect had been the great Imhotep, had a pit burial in the first, Stepped Pyramid.) This pseudo-underground pit burial within the sacred Mound of Creation should enable the King to commune with his familial ancestors, residing forever in the Netherworld, as a worthy substitute for the abandoned subterranean chamber…
The King's sarcophagus, containing the mummified King, would then be the power source for all of the travelling, energized daily - and perhaps nightly, too - by priestly prayers, lustrations and offerings. The ancient Egyptians, it seems, created the first machine for reaching the stars…