Hi Ritva,
Lee: "Note the use of the pyramid determinative after Ax.t-xwfw (third sign after cartouche), and the use of the simple house determinative (Gardiner O1 - last sign within the boxed area) for the word jz (js), "tomb."
'Khufu's Akhet' was written with O24, 'pyramid' det., but Djaty's non royal tomb had the O1 'house' det.
It would be interesting to know if there is any exception to this in the OK - O24 for royal pyramid / funerary complex, O1 for private tomb, but according to the WB, O24 was only used for a non royal tomb from the MK, but no examples from the OK.
So, it seems that in the OK, O24, 'pyramid' det. was used exclusively in the name of the royal pyramid that was also perhaps the name for the whole funerary complex - pyramid, royal cult complex, causeway and 'valley temple'. The cemeteries around Khufu's funerary complex were the cemeteries of Akhet Khufu.
The 'shining' pyramid itself was a manifestation of the dead king, which is why the O24, 'pyramid' det. in the name, seems to have been originally exclusive to the pyramid itself.
The name of Sahura's pyramid / complex, xa-bA-sAHwra: ‘the place where Sahure's manifestation appears’ (J.P. Allen); 'The ba of Sahure gleams' (Edwards)
The names of Snefru's two pyramids at Dahshur, xa-snfrw and xa-rsj-snfrw: ‘the place of Snefru's appearance’, and ‘the southern place of Snefru's appearance’ (J.P. Allen); 'Sneferu Gleams', and The Southern Pyramid 'Sneferu Gleams' (Edwards); 'The Shining Pyramid', and 'The Southern Shining Pyramid' (Baines & Malek)
These names convey the idea of the pyramid itself as a shining manifestation of the king.
According to this PT, the pyramid itself was the Osiris king:
"Atum put your arms around Nemtiemzaf Merenre, around this work (kAt), around this pyramid, as ka-arms; This Nemtiemzaf Merenre is Osiris, this work is Osiris, this pyramid is Osiris." M 225 (N); PT 600; Sethe Vol 2: 375-6 §1657
Piankoff: “The embalmed body of the king lay in or under the pyramid, which together with its entire compound, was considered his body." note: The pyramids were personified (C. Wilke, "Zur Personifikation von Pyramiden," ZÄS, LXX [1934], 56-83), and the title of the queens of Dyn.VI shows that the name of the royal pyramid stood for the name of the deceased himself. Thus the daughter of Unas is the royal daughter of the body of the (the pyramid) ‘Perfect are the Places of Unas’; see P Montet, "Reines et Pyramides," Kemi, XIV (1957), 92-101) (‘The Pyramid of Unas’, Piankoff 1968: 4)
Strudwick 2005: 384-5:
royal mother of the pyramid of Pepi I, Iput
royal mother of the pyramid of [Neferkare]
royal wife of the pyramid of [Meryre]
royal wife of the pyramid of [Merenre]
CT