At several points in the Greek Magical Papyri, certain entities are called upon to represent, embody, or stand at the four cardinal directions.  Little is known about these entities, besides that their names are commonly seen throughout the PGM and other similar magical works as simple barbarous words or divine names generally.  However, in my work, I find that these specific entities are powerful guardians that function not unlike the archangels or watchtowers in medieval and modern Western magic.  Rather than being associated with the four elements, however, these guardians are more associated with the Sun’s stations of sunrise in the East, noon culmination in the South, sunset in the West, and midnight nadir in the North.  Given that much of my work revolves around solar invocations, I find these solar guardians to be powerful allies in my work, and when coupled with guardians of the heights and the depths themselves, many of my rituals have benefited from their presence and protection.  These guardians and parts of these rituals were earlier discussed in this 2013 post and in this 2015 post.

Based on the texts PGM II.64—183 and PGM.XII.14—95, as well as my own explorations of these spirits, I use the following system of names, directions, isopsephic numbers, and descriptions of the solar guardians:

Direction	Name	Number	Description
East	ΕΡΒΗΘ ERBĒTH	124 ΡΚΔ	A winged dragon with a crown of clouds rising above the horizon
South	ΛΕΡΘΕΞΑΝΑΞ LERTHEKSANAKS	321 ΤΚΑ	A falcon with wings fully outstretched wreathed in the fire of the Sun
West	ΑΒΛΑΝΑΘΑΝΑΛΒΑ ABLANATHANALBA	179 ΡΟΘ	A crocodile with the tail of a snake arising from the waters
North	ΣΕΣΕΓΓΕΝΒΑΡΦΑΡΑΓΓΗΣ SESENGENBARPHARANGĒS	1390 ΩΦΠΙ	An infant child sitting atop a blossoming lotus
Up	ΑΚΡΑΜΜΑΧΑΜΑΡΕΙ AKRAMMAKHAMAREI	960 ΩΡΞ	An old balding man dressed in pale grey looking downward holding a ring of keys in his right hand and a staff in his left
Down	ΔΑΜΝΑΜΕΝΕΥΣ DAMNAMENEUS	796 ΨΠΙΕΑ	A young maiden dressed in bright red and hair covered with a red shawl looking forward holding a spear in her right hand and a torch in her left
Center	ΜΑΛΠΑΡΤΑΛΧΩ MALPARTALKHŌ	1983 ΩΨΥΠΓ	A luminous being

It has been indicated to me that the guardians of the four cardinal directions, the “true” solar guardians, are not entirely distinct entities.  They are no more separate than the four cardinal points on a circle are separate; while they may represent different directions, they are still part of the same path.  They may be considered as stations, managers, or reflections of the Sun in its stations at the four corners of the world: though they may still be distinct with their own unique presences and powers, they are still part of the same overall group or synaxis.  As such, these four entities are best called together, though one will usually predominate over the others, specifically the one that represents the quarter of the sky that the Sun is currently in.

Note that, technically, that Akrammakhamarei and Damnameneus, the guardians of the heights and depths respectively, don’t appear in any traditional source along the other four guardians of the cardinal directions, and their descriptions are very different compared to those of the cardinal direction guardians.  This is an innovation on my part, because I felt that having guardians for the directions of above and below completed the overall system, although they respond in a different way and have a different type of power rather than those of the four cardinal directions.  Note that, strictly speaking, only the four guardians of the cardinal directions are distinctly solar in nature, while those of above and below are more like realm-rulers or guardians of space rather than the Sun.

In addition to all these, I also recognize a seventh quasi-guardian, that of Malpartalkhō.  This isn’t a true solar or spatial guardian, but is a special name I was given to use to refer to the guardian of the one who perceives the Sun in the middle of all the directions, which is to say the magician themselves, which is to say you.  In a sense, this name functions as as a kind of generic “higher self” name; originally, I had thought to use the name of one’s own natal genius, agathodaimon, HGA, or other similar tutelary spirit, but I find that Malpartalkhō works better for these invocations.  If desired, such a name may be mentally intoned while physically intoning the name Malpartalkhō.  Because of this, there is no true description for Malpartalkhō, because it represents your own divine presence.

A simple, short invocation for the guardians of the directions starts by facing East, and can be used to quickly call upon the support and protection of the guardians of the six directions.  The only gesture that needs to be used, if one is used at all, is pointing the hand with the fingers outstretched in the direction specified:

ΙΩ ΕΡΒΗΘ, take thy place before me!
ΙΩ ΑΒΛΑΝΑΘΑΝΑΛΒΑ, take thy place behind me!
ΙΩ ΛΕΡΘΕΞΑΝΑΞ, take thy place at my right!
ΙΩ ΣΕΣΕΓΓΕΝΒΑΡΦΑΡΑΓΓΗΣ, take thy place at my left!
ΙΩ ΑΚΡΑΜΜΑΧΑΜΑΡΕΙ, take thy place in the heights!
ΙΩ ΔΑΜΝΑΜΕΝΕΥΣ, take thy place in the depths!
For I am ΜΑΛΠΑΡΤΑΛΧΩ, standing in the midst of the All!

The short invocation, with the sacred names transliterated into Roman script (which can also serve as a key for transliterating the other invocations given below):

IŌ ERBĒTH, take thy place before me!
IŌ ABLANATHANALBA, take thy place behind me!
IŌ LERTHEKSANAKS, take thy place at my right!
IŌ SESENGENBARPHARANGĒS, take thy place at my left!
IŌ AKRAMMAKHAMAREI, take thy place in the heights!
IŌ DAMNAMENEUS, take thy place in the depths!
For I am MALPARTALKHŌ, standing in the midst of the All!

Such a short invocation may be used to quickly establish the spiritual bounds of a ritual area without too much ceremony.

Another form of short invocation is slightly more involved, and involves saluting each guardian in turn following the directions of the path of the Sun from a perspective in the Northern hemisphere: East, South, West, and North, followed by saluting the heights and then the depths.  For those in the Southern hemisphere, the recommended order would be East, North, West, and South, then the heights and the depths.

1. First, face the East or, if preferred, whatever quarter of the sky the Sun happens to be in at the moment of the invocation, and calm and center the breath.
2. Take a half-step forward with the right foot, kiss the palm of the right hand, and raise the hand up and out towards that direction.  Give the salutation to the guardian, lower the hand, bring the right foot back, then turn 90° clockwise to salute the next guardian.  Visualize each guardian as you salute them materializing and filling that quarter of the sky.  The four salutations for these guardians are, with the order to be changed according to the direction first started with:
   

   ΙΩ ΕΡΒΗΘ, take thy place in the East!
   ΙΩ ΛΕΡΘΕΞΑΝΑΞ, take thy place in the South!
   ΙΩ ΑΒΛΑΝΑΘΑΝΑΛΒΑ, take thy place in the West!
   ΙΩ ΣΕΣΕΓΓΕΝΒΑΡΦΑΡΑΓΓΗΣ, take thy place in the North!

3. Once all four guardians of the cardinal directions have been saluted, return to the original direction, and stand with both feet together.
4. Visualize the guardian of the heights, kiss the palm of the right hand, look directly up and extend the right palm outwards and upwards to salute the guardian of the heights:
   

   ΙΩ ΑΚΡΑΜΜΑΧΑΜΑΡΕΙ, take thy place in the Heights!

5. Visualize the guardian of the depths, kiss the palm of the right hand, look directly down, and extend the right palm outwards and downwards to salute the guardian of the depths:
   

   ΙΩ ΔΑΜΝΑΜΕΝΕΥΣ, take thy place in the Depths!

6. Visualize all six guardians around, above, and below you, face forward, extend both arms outward with the right hand turned up and the left hand turned down, and give the concluding call:
   

   For I am ΜΑΛΠΑΡΤΑΛΧΩ standing in the midst of the All!

As opposed to the shorter invocations of all the guardians at once, a series of long invocations may instead be made that more fully invoke each guardian in a more ritualized form.  Instead of calling upon six guardians separately, only the main four are called upon, with Damnameneus and Akrammakhamarei being referred to as realms instead of guardians.  These four invocations may be made in quick succession, facing each of the four directions of the Sun’s passage (East, South, West, and North), or they may be made separately at the times of sunrise, noon, sunset, and midnight in the same manner as the Thelemic solar adorations of Liber Resh.  As before, one should face the direction of the four guardians of the cardinal directions, salute them with the right hand and right foot extended, and visualizing them with detail and clarity.

The sunrise invocation of Erbēth:

ΙΩ ΕΡΒΗΘ, you who are Helios who rise now from the realm of ΔΑΜΝΑΜΕΝΕΥΣ into the realm of ΑΚΡΑΜΜΑΧΑΜΑΡΕΙ, who whose form is a winged dragon with a crown of clouds, take your place in the East as you move from the North, quelling all discord as you bring bright force to dark space!
For I am ΜΑΛΠΑΡΤΑΛΧΩ standing before you, calling upon you who are ΕΡΒΗΘ!

The noon invocation of Lertheksanaks:

ΙΩ ΛΕΡΘΕΞΑΝΑΞ, you who are Helios who surmount now onto the highest heights of the realm of ΑΚΡΑΜΜΑΧΑΜΑΡΕΙ, you whose form is a royal falcon ringed in golden fire, take your place in the South as you move from the East, sending upon us radiant fire and life-giving heat!
For I am ΜΑΛΠΑΡΤΑΛΧΩ standing before you, calling upon you who are ΛΕΡΘΕΞΑΝΑΞ!

The sunset invocation of Ablanathanalba:

ΙΩ ΑΒΛΑΝΑΘΑΝΑΛΒΑ, you who are Helios who sink now from the realm of ΑΚΡΑΜΜΑΧΑΜΑΡΕΙ into the realm of ΔΑΜΝΑΜΕΝΕΥΣ, you whose form is a snake-tailed crocodile peering above the waves, take your place in the West as you move from the South, shedding cold water as you cleanse hot day with cool night!
For I am ΜΑΛΠΑΡΤΑΛΧΩ standing before you, calling upon you who are ΑΒΛΑΝΑΘΑΝΑΛΒΑ!

The midnight invocation of Sesengenbarpharangēs:

ΙΩ ΣΕΣΕΓΓΕΝΒΑΡΦΑΡΑΓΓΗΣ, you who are Helios who settle now into the darkest depths of the realm of ΔΑΜΝΑΜΕΝΕΥΣ, you whose form is the holy infant upon the lotus seat, take your place in the North as you move from the West, reborn as king from the virgin womb of the world!
For I am ΜΑΛΠΑΡΤΑΛΧΩ standing before you, calling upon you who are ΣΕΣΕΓΓΕΝΒΑΡΦΑΡΑΓΓΗΣ!