The final consideration to take into account the projection of 36 degree geometry at Giza, and the one that relates most directly to the placement of the Sphinx at this central point, is the measure and determination of the angle given as that of 'Astronomical Twilight' which is a constant projected to 18 degrees below the horizon at sunrise or sunset were the Sun is no longer casting any illumination above the horizon.

Effectively then the angle of 'Astronomical Twilight' to the 90 degree zenith of the sun at Mid-day is 108 degrees from beneath the horizon. and it is this 18 degree angle which is found in iconography relating to the sphinx and the essential key to the geometry at Giza, and it would seem certain that this was an aspect of the Sphinx cult.

In terms of measuring this angle, then it would seem likely that the Egyptians would have had to record a corresponding period of time from when the period of twilight was first observed before breaking the horizon, to the degree correspondant in terms of ascendancy above the horizon.

Thus to determine the projected 18 degree angle benath the horizon one finds the corresponding angle above the horizon of 18 degrees determined through the measure of elapsed time. Thus the associated angular projections of the phenomena are the 18 degree angle projecting below and above the horizon to form the 36 degree angle. The precise determination of these angles would have been critical to the Egyptians as the place beneath the horizon would be the location were the sun began to emerge from the Duat or was seen as fully entering within, rather than the actual point upon the horizon, the twilight zone would also be the time of best viewing for Mercury and Venus as Morning/Evening stars.

Mercury had the simplest name of the planets, Sbg, though its meaning is unknown. It was frequently associated with Seth, the enemy of Horus and murderer of Osiris. A text which dates to the era of Ramses VI (1148-1138 B.C.), refers to Mercury as "Seth in the evening twilight, a god in the morning twilight," conclusively showing that it was recognized as the same object in both the morning and evening.

http://filer.case.edu/~sjr16/advanced/pre20th_ancients_egyptians.html

To furthur understand these geometric considerations and to evaluate a precise centre for the Giza Plateau schemata, the activities of the 18th Dynasty in the locale can provide surprising illumination, when one considers the Temple built in the vicinity of the Sphinx by Amenhotep II and the Dream Stela erected by his son Tuthmosis IV.

http://www.touregypt.net/featurestories/sphinx3.htm

The 18th Dynasty had renewed interest in the site which had fallen into neglect over the centuries since initial construction. and when one looks at the postitioning of the Temple erected by Amenhotep II one finds that the entranceway is aligned at a 45 degree angle toward the centre of the head of the Sphinx, a radical departure in itself from aligning to the cardinal directions.

One also finds that the angles projecting toward the Temple corners from the intended alignment point on the Sphinx's head are each at 9 degrees forming the 18 degree angle, either side of this 18' degree convergance toward the corners are angles of 36' set against the vertical/horizontal axis toward the cardinal points.

In terms of measuring and observing these angles, then it can be noted that sundials from around 1500 BC measure the 9 degree angle as it is correspondent with the first hourly increment of the six hour period toward mid-day, the 18 degree angle is not one of the angles of hourly increment, but would have been noted in the same way in accordance with time elapsed since sunrise relative to first twilight, but not on an hourly incremental sundial, the first example of which known dates to the time of Tuthmosis III

Egyptian Sundials.

Ostensibly then that's quite a straightforward orientation of the Temple dedicated to the Sphinx, just to project the entrance right between the eyes as it were, but the positioning is actualy more subtle...

As previously discussed the overall site plan of the Giza plateua of ten directional 36 degree angles was seen to be projecting from between the paws of the Sphinx, not the head, and quite possibly the Sphinx was set up as a guardian of this centre watching over the point directly between it's front paws, it is actualy the South-Eastern wall of the 18th Dynasty Temple which runs in alignment to this forward point between the paws, and also from here an angle of 18 degrees to the North-South axis runs through the entranceway to the Temple corner, the orientation of the sphinx was of extreme importance in terms of the cults associated with it;

Then the hour came to give rest to his followers, at the limbs of Harmakhis, beside Sokar in Ra-Setjaw, Renutet in Northern Djeme, Mut the mistress of the Northern Wall and the mistress of the Southern Wall, Sekhmet who presides over her Kha, Seth, the son of Heka, the Holy Place of the First Occasion (of creation), near the Lords or Kheraha, the divine road of the gods towards the West of Heliopolis.

Now then, the great statue of Khepri was lying in this place, great of power and powerful of majesty, the shadow of Re resting upon it.

These are no secondary considerations, for it is this incorporation of aligning to the central point between the paws that finds the original conceptual centre, one way or another Amenhotep has realised the significance of this point

The 18 degree projections from this point are therefore in alignment with the siting of the earlier Valley Temple of Khafre and the Sphinx Temple,, and whilst these buildings were in neglect and generally buried by the time of the 18th Dynasty such that viewing platforms could be built upon the mound that was formerly the Sphinx Temple, the true point has still been realised, and within the paws of the sphinx a centre of worship was established. The 18th Dynasty showed little regard for the Sphinx and Valley temple yet given their tendancy to focus on the sun placed great importance to the monument associated with the geometry of it's rising.

The Altar placed at this Chosen Place is said to date from the time of Ramasses II

The kings of the 18th Dynasty showed deep respect for the pyramids as monuments of their ancestors at Giza, and the area gained considerable religious significance as the center of royal worship to the Great Sphinx, "Lord of Setpet, the Chosen Place." Princes and kings of the 18th and 19th Dynasties erected stelae between the paws of the Sphinx, which was no longer seen as a royal statue but rather as an image of the sun god Harmachis, "Horus in his Western Horizon", which was actually a reference to the "Horizon of Khufu". Amenhotep II dedicated a small temple to Harcachis to the northeast of the Sphinx. On foundation tables of that temple, the Sphinx is also named Harmachis-Hauron. Hauron was the name of a Syrian-Palestinian god of the netherworld that a community of Syrian-Palestinians living near the Great Sphinx identified with his image. Ramesses II installed a sanctuary within the forepaws of the Sphinx.

http://www.touregypt.net/featurestories/giza.htm

After uncovering all the hinder portion of the Sphinx, Caviglia found at the end of the long passage which lay between the paws, a small temple, ten feet in length by five in breadth, immediately below the chin of the figure. The extremity of it was occupied by a block of granite, fourteen feet in height, covered with sculptures and hieroglyphics recording the name of Thothmes IV; this block is the stele of which we are about to give a translation.

It was set up against the breast of the Sphinx, without, however, actually touching it. The two walls, built along the paws at right angles to that at the end of the shrine, had been adorned with two other stelæ of smaller size and of limestone; one of them, containing the name of Ramses II, was still in situ, the other had fallen into the interior of the chapel among other masses of rubbish, in which fragments of the beard once attached to the chin of the figure, as in the case of all Egyptian figures of gods or kings, could still be recognised. A door opened between the two walls of lesser elevation which enclosed the shrine on the eastern side. Before the temple, a sort of paved court extended about three-fourths of the length of the paws, and was also enclosed by two walls separated from one another by a roofless opening before which was erected a square altar of granite.

http://www.dabar.org/RecordsOfThePast/Vol2/SteleThothmes-4.html

The 'Sphinx Temple' itself was designed such that in the central open courtyard provision was made to erect the statues of ten colossal Deities upon pedastals, from the central point of the Temple this ten-fold division in accordance with the pedastals for the ten can be observed. Thus the Temple before the central position of the entire basic sub-division into ten shows correspondance with this principle. Around this are twenty-four columns, probably to be associated with the twenty-four hour subdivision of the day, the central ten being relative to the Celestial divisions. There are also indications that incorporate into the architecture are the alignments to Sirius and Orion rising, though the Temple itself woluld essentialy block this view from the central position between the paws of the Sphinx, yet the possibility remains that this was symbolicaly incorporated, and that once there had been more simpler sighting arrangements in the locale, the elevated position of the Sphinx itself though would have had an overview of these relative positions toward the horizon http://oi.uchicago.edu/OI/DEPT/COMP/GIZ/MODEL/Giza_Model_Fig15.html

Emerging from their rest houses near the Valley Temple, Egyptian royalty descended a stairway to a broad viewing platform built over the buried Sphinx Temple immediately in front of the Sphinx. After ritual stops at shrines and podiums, they descended farther to the heart of the cult—a small chapel between the paws of the giant statue.

After making offerings to the god, the pharaoh must have felt he was linked back to the primordial god-king, Hor-em-akhet, who towered above him.

Evidence indicates that while this reverence for the Sphinx excelled anything previously shown for the statue, New Kingdom workers were recycling stone from other monuments at Giza. They were even stripping stone from the causeway that ran from Khafre’s pyramid to his Valley Temple to use in repair of the Sphinx.

The famous Dream Stele of Thuthmose IV is a recycled lintel of a doorway from Khafre’s Pyramid Temple.

http://www.aeraweb.org/sphinx_park.asp

The siting of the centre of the design of the geometry of the Giza Plateau between the front paws of the Sphinx finds accordance in the Dream Stela, the centre of the Pentagonal star that projects from the 18 degree angles above and below the central horizon plane, as circled in blue on the diagram, is this point.

I've also indicated in yellow the 9 degree angle correspondant to the first (and 11th )hour of the day, this projects toward the eyes of those making offerings at these hours, in the same manner the 18 degree angle projects toward the eye of the Sphinx

It is toward the eye of the sphinx that the 18 degree line above the horizon projects, as this is relative to observing the sun at the correspondant angle of ascendancy, and one finds other examples of this angle rising from between the two lions that face toward the horizon. toward the observant eye such as in 'The Book of the Earth', which incorporates the 18 degree angle in connection with the rising of Ra-Osiris.

http://www.touregypt.net/featurestories/bookofearth.htm

"I am Horus, the great Falcon upon the ramparts of the house of him of the hidden name. My flight has reached the horizon. I have passed by the gods of Nut. I have gone further than the gods of old. Even the most ancient bird could not equal my very first flight. I have removed my place beyond the powers of Set, the foe of my father Osiris. No other god could do what I have done. I have brought the ways of eternity to the twilight of the morning..."