The Kālacakra maṇḍala according to the Vajrāvalī of Abhayākaragupta

1. Drawing the maṇḍala

Perhaps the most important of the original Indian sources on the drawing of the Kālacakra maṇḍala, and one that is important to all the Tibetan traditions, is the Vajrāvalī-nāma-maṇḍalopāyikā (dkyil 'khor gyi cho ga rdo rje phreng ba) of Abhayākaragupta, an abbot of Vikramaśīla monastery, probably in the late 11th or very early 12th century CE. This text gives the details of how to prepare for the purpose of giving empowerment, 26 maṇḍalas.

Many Tibetans have elaborated on the methods given in the Vajrāvalī, and the tradition is very much still alive, particularly the transmission of the Kālacakra, although some frown on the Vajrāvalī Kālacakra because it allows the use of a painted rather than powder maṇḍala. This is considered by critics to be improper.

This article will describe the method of drawing the maṇḍala according to the Vajrāvalī and is based on three main sources: the most important of these is the Vajrāvalī itself, but I shall also refer to two Tibetan descriptions of the Vajrāvalī method. One of these is from the Jonang tradition, and is given by Banda Gelek in his text "The Illuminating Sun rays" (rje sgrol ba'i mgon pos mdzad pa'i dkyil chog rgya mtsho'i thig tshon gsal byed nyi ma'i 'od zer). The other is in the Gelug tradition, by Akhuching Sherab Gyatso: "bla ma rdo rje 'chang chen pos dkyil chog rdo rje phreng ba sogs kyis mtshon pa'i nyer mkho'i thig dang bshad pa phyag len du ma'i skor la brjed byang mdzad pa". Any particular comments made by Sherab Gyatso, and there are several, are indicated by "SG:"

Units and dimensions

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The description starts by defining the overall dimensions of the maṇḍala and the units to be used in its construction. The first thing that needs to be done is to draw the central (tshangs thig, brahmasūtra) and diagonal lines (zur thig, koṇasūtra). In Abhaya's description, these lines only extend to the inner bounding circle of the perimeter of earth. There are six such perimeters surrounding the maṇḍala, that of earth being the innermost. In practice, these main lines need to be drawn longer than this, but taking Abhaya's definition, each of these lines, measured from the centre to the inner circle of the earth perimeter, is eight cubits. The size of the maṇḍala is stated to be four cubits – this is the distance between the inside of the walls of the body palace.

In a ritual context, the width of the presiding teacher's thumb is determined and 24 such finger-widths is one cubit. Half of one of these finger-widths is called a minor unit (cha chung); these are the main units used in describing the maṇḍala. Other units that are sometimes used are door units (sgo tshad, DU). The maṇḍala consists of three palaces, and the door unit for any palace is the width of the doorway of that particular palace. The mind palace is the smallest of the three, and its door unit (mind-DU) is equal to six minor units (mu). The speech palace is twice the size, and so one speech-DU is equal to 12 mus. The body palace is again twice the size, and so one body-DU is equal to 24 mus. The inner widths of the three palaces are, respectively: 48, 96 and 192 mus. Incidentally, in most other maṇḍalas, such as all the other maṇḍalas described in the Vajrāvalī, a minor unit is defined as one quarter of a door unit.

(Pic 1)The first part of the construction is to draw the main lines, and then start measuring out the position of the walls, and so forth. For this initial description I shall follow Banda Gelek.

Having prepared the surface on which the maṇḍala is to be drawn, first, draw the east-west central line, and having found its centre, describe from that centre a circle of radius 8 body-DU. This is 192 mus, and forms the innermost boundary of the earth perimeter. From where that circle meets the central line, draw intersecting arcs of larger radius. Where these arcs cross draw the second central line, running north-south. These steps are illustrated in the diagram on the right.

(Pic 2,3)Then, where the two central lines meet the original circle, draw further intersecting arcs using the previous radius of 8 body-DUs. Connect these together in order to form the two diagonal lines. In practice, one would first need to measure out the total area that is to be used for the maṇḍala. If the diameter of the inner bounding circle of the earth perimeter is 384 mus (2x192), that of the outer bounding circle of the outermost perimeter is 624 mus.

(Pic 4)Banda Gelek's description takes the distance from the centre to the extreme edge, 312 mus, and divides this into 13 equal parts. Each of these is 24 mus, or 1 body-DU. Next, draw a circle with a radius of 8 1⁄2 body-DUs (204 mus) and connect the points where this circle intersects the diagonal line to form a square. Clearly, the diagonal lines and at least one central line need to be longer than the standard 8 body-DUs. The lines forming this square are the parapet lines (mda' thig, pārśvasūtra??? Mori, 74) for the body maṇḍala, and should each be 288 mus. There is actually a very small error in creating the square this way, but that error is small enough to ignore; if accurately drawn, the sides of the square will be 288.5 mus. (By Pythagoras' theorem: 2042 ÷ 2 = 144.252.) However, this method helps ensure a properly square shape.

(Pic 5)The next step is to divide the diagonal lines from the corners of this square to the centre into 12 equal parts.

(Pic 6)Draw further squares by connecting the first, third and sixth positions from the centre. From the centre, we now have four squares forming: the outer line of the outer beams of the circle of great bliss, and the parapet lines of the mind, speech and body palaces. All these squares are final lines and not construction lines, and so they will not need later to be erased. According to Banda Gelek's interpretation, the method of the Vajrāvalī is intended to do away with construction lines; the descriptions in the Tantra and Vimalaprabhā require many to be drawn, if taken literally. However, it is impossible to do away with construction lines completely. These steps are illustrated in the diagrams on the left

(Pic 7)Measuring out from the centre, first a circle is drawn with radius 2 mus; this is for the receptacle of the central lotus. Then, measure out along the central lines, 4, 1, 4 and 1 mus, drawing squares, again with their corners on the diagonal lines. The 1 mu spaces between the first two of these squares and the outer pair form the inner and outer beams of the circle of great bliss. Abhaya refers to these as vajra-garlands, after the design that will later be drawn on them. Another circle also needs to be drawn inside the inner beams, of radius 6 mus. This forms the space for the eight petals of the main lotus.

Lines now need to be drawn in the 4 mu space between the second and third squares beyond the lotus. For these, measure right and left of the central lines, 2, 1, 3 and 1 mus. The 4x4 square cells that are formed in the cardinal and intermediate directions need to have eight-petalled lotuses in them of 4 mus diameter. As with the main lotus, the diameter of the receptacle of each lotus is one third the overall diameter. The other cells formed between these are for flasks.

Beyond the outer of the four squares forming the beams, measure along the central lines 7 and then 4 mus, drawing further squares. These form the deity-podium of the mind palace. Then measure 1 mu further and draw another square. This is the base line (rtsa thig, mūlasūtra) of the mind palace; the base line is the inner line of the walls. Parts of this line need to be removed to form the doorway, 3 mus either side of the central line, giving the doorway a width of 6 mus.

(Pic 8)Lines are now drawn to form the porch. This consists of three sections: the porch-projection (sgo khyud, niryūha), the porch-extension (sgo 'gram, kapola) and porch-sides (sgo logs, pakṣaka). Each of the lines now to be drawn are 6 mus in length. From the point of view of the diagram, first, from the end of the base line up parallel to the central line, then horizontally away from the base line, and then again up parallel to the base line. That last line ends on the parapet line for the mind palace, drawn earlier.

(Pic 9)Further lines now need to be drawn between the base and parapet lines. The first should be the outer line for the walls; this is parallel to the inner wall line that has just been completed, and 1 1⁄2 mus from it. It follows the shape of the porch components. Next to the porch-sides are the pillars for the toran. These are 1 1⁄2 mus wide and 7 1⁄2 mus in length. For each of these, just one line needs to be drawn parallel to the central line. Further lines then need to be drawn parallel to the base line. Measuring up from the outer wall line: 3, 1 1⁄2, 3 and 1 1⁄2 mus.

(Pic 10)These form the spaces for the plinth (stegs bu, vedika), jewelled frieze (rin po che'i pha gu, ratnapaṭṭika), garlands and drops (dra ba dang dra ba phyed pa, hārārdha hāra), pipes (rin chen shar bu, bakulī) and parapet (mda' yab, kramaśīrṣa). The walls are actually more complicated than described here, consisting of parallel walls. This is described later in the Vajrāvalī and not mentioned at this point in the description.

(Pic 11)The toran (rta babs, toraṇa) extends beyond the parapet line for 3 DUs, and consists of three sections, or stages. Abhaya describes them by giving the size of each stage, in height, in the direction of the centtral line. Each stage consists of a supporting beam, railing (myos pa srung ba, mattavārana) and four pillars. The first stage has a height of 6 mus, the second 4 1⁄2 and the third 3 1⁄2. On the very top is the roofing and flask top, with a height each of 2 mus. Added together, this gives a total of 18 mus, or, 3 DUs.

A total of 12 horizontal lines need to be drawn of varying lengths. For these, measure out from the parapet line: 1, 1, 4, 1⁄2, 1, 3, 1⁄2, 1, 2, 1⁄2, 1 1⁄2 and 2 mus. These lines extend either side of the central line, respectively: 12, 8, 9, 9, 6, 7 1⁄2, 7 1⁄2, 4, 6, 6, and 4 mus.

There are only eleven in that last list. The last line is for the top of the flask that sits on top of the toran. Banda Gelek gives this a length of 2 mus, as does Tāranātha. But neither the Vajrāvalī nor the Vimalaprabhā give any length for this line. Sādhuputra (author of one of the few surviving Indian maṇḍala rituals) also does not give this in his maṇḍala description. So where does this come from? In one text Dolpopa gives no length for this line, and yet in another he gives it as 2 mus. This maybe where this idea originated. But why?

The Vimalaparabhā, as with the description above and and most other texts, first gives the positions of these horizontal lines and then their lengths. When describing the lengths it simply says "above this, by two, is the flask". The flask is 2 mus in height, and I would read this as simply a restatement of that height, but it is possible that Dolpopa or others took this to be an indication of the length of the line for the top of the flask. All Jonang writers and many others have subsequently followed this.

(Pic 12)However, I am yet to see a maṇḍala that actually uses this size for the top of a flask, with the width at the top the same as its height; this would seem quite unappealing. For this reason, in the diagrams here the top of the flask is given an arbitrary width, starting at 1 mus in the diagram to the right.

The next step is to draw vertical lines to complete the structure. Counting from the bottom, the first line defines the main beam of the first stage, and vertical lines need to be drawn from its ends, down to the line below it – the parapet line. The same is done with the second line which defines the railing. Between lines two and three, eight vertical lines are drawn for the pillars, each of which is 1 mu wide, creating three cells for offering goddesses, each 4 mus across. A similar process is followed for the second stage, with the pillars each being 3/4 mu wide and the cells 3 mus across. And again for the top stage, with the pillars each 1⁄2 mu in width and the cells 2 mus across.

Vertical lines are then drawn between the ends of lines nine and ten to form the beam for the roof, and lines are drawn from the ends of line eleven to points on line ten, 5 mus either side of the central line, to form the roof. Finally, the flask is drawn on top, with victory banners either side.

Perhaps the most famous of all śālabhañjikā, supporting a toran beam at the great stupa of Sanchi.

During this description, Abhaya adds some further details. Beside the outer pillars of the first stage are (SG: white) elephants supporting (SG: blue) lions that support the beam of the second stage. Similarly for the second and third stages, beside the outer pillars are śālabhañjikā supporting the beams above. Abhaya simply calls these goddesses; the specific term śālabhañjikā is used in the Vimalaprabhā. Many Tibetan writers and artists seem to have been confused by these, even suggesting that they can be male figures. They are a very common motif in Indian architecture. The figure usually has one leg crossed in front or behind the other, and with one hand bending down the branch of a tree. The Buddha's mother is represented in a very similar pose in depictions of the birth scene. The final details given for the toran are that from the ends of all beams hang bells, chowries, mirrors, victory banner and flags.

(Pic 13)The construction now starts for the speech palace. The base line for the speech palace is 12 mus beyond the parapet line of the mind palace, and the dimensions of all the wall components from the base line up to and including the toran are all twice those of the mind palace. A deity-podium is needed between the mind parapet line and the speech base line. For this, just as with the mind palace, measure out from the mind parapet line 7 and then 4 mus, drawing squares. These form the podium, with a 1 mu narrow gap between the outer edge of the podium and the speech base line. This podium needs eight lotuses, each of diameter 4 mus and with eight petals. These are in the four corners and in the middle of each side of the podium, coinciding with the middle cell of the middle stage of each of the mind palace torans. The middle cells are 3 x 3 mus in size, and as the lotuses need to have their diameter of 4 mus, sections of the pillars and railing of the toran are cut away to accomodate the lotus.

(Pic 14,15)The body palace is next. The base line for the body palace is 24 mus beyond the speech parapet line, and the dimensions of all the wall components from the base line up to and including the toran are all twice those of the speech palace.

As with the speech palace, a deity-podium is needed within the body base line. For this, measure out 11 and then 12 mus, drawing square construction lines for the podium. This leaves a small gap of 1 mu between the outer edge of the podium and the body base line. The podium needs 12 lotuses, each of diameter 12 mus. Four of these are in the four corners, and the other eight are in pairs, right and left of the doorways – right and left of the speech toran, which is drawn over this body palace deity podium. None of my Vajrāvalī source texts give an exact position for these lotuses, but in his general Kālacakra maṇḍala description, Banda Gelek says they are 27 2/3 mus right and left of the central lines. That is how they are shown in the diagrams here.

These lotuses have three bands, or rings, of petals: the inner band has four, the middle eight and the outer 16, a total of 28. The bands are all equal in width, and that width is the same as the diameter of the receptacle. In order to draw these, a diameter of the lotus is divided into seven equal parts, and three circles drawn, centred on the middle point and passing through the others. An important point to note is that in each ring of petals, one petal needs to be in a line with the centre of the maṇḍala. For those on the corners of the podium, this simply means that in each ring one petal must lie centred over the diagonal line. With the other lotues, the same applies, but they are not turned through small angles in order to line up with the centre of the maṇḍala. Instead, they are drawn so that the petals line up parallel to the central line. This should be clear in the diagrams on the right.

In the middle of the doorways of the body palace, just beyond the tips of the flasks on the speech palace torans, are drawn the chariots for the protective deities. These are 12 mus in size, and are usually interpreted as being square, although they are often drawn as rectangular, with the longer side 12 mus. Another point made by Abhaya is that the tips of the body toran flasks reach to the middle of the water perimeter; the perimeters are to be drawn next. Points like this are often made in the descriptions for maṇḍala drawing, often as a check that drawings have been made accurately. Another common point made regarding the body torans is that the centre point of top line of the railing on the top stage of the toran should coincide with the end of the central line, exactly at the circle that is the inner boundary of the perimeters, which has a radius of 192 mus. (As described earlier, strictly speaking, the central lines end at that point, although in practice they are often drawn longer.)

From that circle, we then measure out: 12, 24, 24, 24, 12 and 24 mus. The bands formed are for the perimeters of earth, water, fire, wind, space and the garland of light ('od zer gyi phreng ba, vajra-fire in the Vimalaprabhā). The final outer circle gives the maṇḍala an overall diameter of 624 mus.

This completes the construction for the maṇḍala. Other details are needed, but these are described in another section of the Vajrāvalī, together with the colours.

Colours

The ground that is within the two vajra-garlands of the mind maṇḍala – the square sets of beams – is all black, as is the eastern ground in all three palaces. (SG: The ground within the tathāgata-dais and the pillars is blue.) The eastern ground refers to the eastern ground between the diagonal lines. (This may seem obvious, but other definitions have apparently been in use.) The ground of all three palaces is in the south, red, in the west, yellow and in the north, white. The ground includes the small gaps between the podium and the base line of the next palace.

Of the wall structures, the plinths are white, the frieze is red and adorned with various coloured jewels (often in the shape of deep blue triangles, red semi-circles, yellow squares and white circles). The garlands and drops are white on a black background. This is also the case with the pipes (drawn like upside-down bottles) and the merlons of the parapet; the latter are designed like half lotus petals (that is the description used in Tibetan, but in practice they look nothing like lotus petals). The main toran pillars, either side of the doorways, are yellow. (SG: The corners of the walls are adorned with crossed-vajras that are white.)

The central lotus in the mind palace is green. The inner vajra-garland and the pillars are all black. The pillars in the east are decorated with black swords, in the south with red jewels, in the west with yellow wheels, and in the north with white lotuses. The eight flasks are drawn in the 3 mu-wide cells between the pillars, and are coloured white, each seated on a lotus and topped by a lotus.

The outer vajra-garland is green. The deity-podium is white (the current description is for the mind palace, but this is true of all three palaces). The walls of the mind palace are triple, from the inside, white, red and black. (SG: Has green instead of black. This is presumably an error; other authors, such as Ngawang Lozang Choden, ngag dbang blo bzang chos ldan, author of the main Vajrāvalī empowerment text used in the Gelug tradition, have black.) There are small gaps between these, and in order to draw them, the 1 1⁄2 mu space drawn for the walls is divided into eight equal parts. (Abhaya actually says nine, but this seems just to be a different grammar for making the division; it only works if you divide into eight parts.) Each wall takes up two of the narrow bands thus formed, and this leaves two gaps of one band in width between the walls. It is not stated in the texts, and it would be a very small detail to paint, but the gaps between the walls should be the colour of the directions; the colour of the ground.

The sides of the door-extensions are adorned with vajras and jewels.

All twelve torans are multi-coloured. (SG: The lower beams of all toran are green, the railings are red and all pillars yellow. The beams for the upper two stages are blue, the beam for the roof is red and the roof itself is blue. For the backgrounds of the cells of the torans: all the lower cells are blue; all the upper cells are green; for the middle cells: in the mind toran they are blue-green, for the speech, the middle cells are green and right and left red, the body all are white. Each mind and speech toran has only drawings of jewelled garlands as ornaments. The flasks on top of all torans are red, each topped with a jewel. For the other toran, in the three middle cells are offering goddesses, carrying offerings and in the three upper, simply jewel garlands.)

The speech podium is white. The lotuses on it do not have sun or moon disks for seats. The lotuses in the cardinal directions are red, and those in the corners are white. The walls of the palace are five-fold, and these are, from the inside, green, black, red, white and yellow. The space for the walls is divided into 14 equal bands, and as before, two bands are alloted to each wall, leaving four single bands between the walls.

The podium and the walls are coloured in the body palace the same as the speech palace. The lotuses on the body podium are also without moon or sun seats, and those in the corners are white and all the others red.

On the body palace plinths, underneath the main toran pillars, are pairs of seats (of the four elements) for the nāgas. These each have a size of 12 mus. In the east these are black, circular and have victory banners drawn on them; in the south they are red, triangular and with svastikas; in the west they are yellow, square and with vajras; and, in the north they are white, semi-circular and with lotuses. Many Gelug painted maṇḍalas will show the element disks in the north and east the other way around. This is presumably because they are given this way in the sādhana by the 7th Dalai Lama. Associating the semi-circular design with wind and circular with water is the normal Buddhist tradition. The reverse is particular to Kālacakra. Most writers state that it does not matter which method is followed.

To the right of the nāga seat right of the eastern doorway is a flask of nectar representing the above nāga, Jaya; to the left of the square nāga seat left of the western doorway is another flask of nectar representing the below nāga, Vijaya.

In the central cell of the lower stage of the eastern body toran is a black dharmacakra; right and left of this are black male and female deer (this is usually interpreted as suggesting they are in the right and left cells, but some consider all three to be in the central cell). In a similar position in the south is a red "excellent flask", with a conch to the right and a red lotus to the left. In the west is a yellow bodhi-tree, with a kinnara and kinnarī. In the north is a white great drum with a club and hammer.

In the Gelug tradition, dharmacakras are used for the charnel wheels, with pairs in the east and west.

The ground between the parapet and the inner edge of the perimeter of earth is black, and should have many various offerings drawn on it. This area is often referred to as the offering ground (mchod pa'i sa gzhi).

The earth perimeter is yellow, and in its NE is the disk of the rising full Moon, with a diameter of 12 mus. In the SW is the disk of the setting Sun, also 12 mus. At the exact NE and SW positions, the corners of the body parapet overlap the earth perimeter, and so the Sun and Moon have to be drawn just to one side of these corners.

The water perimeter is white (SG: with blue designs), the fire perimeter red, the wind perimeter black. On the junction of the fire and wind perimeters are eight eight-spoked charnel ground wheels with diameters of 12 mus. Those in the cardinal directions are red and in the intermediate directions white. (The charnel ground wheels (dur khrod kyi 'khor lo) are interpreted differently. Some draw these as dharmacakras and other as wrathful weapon wheels; the latter seems more appropriate for the charnel ground seat of a wrathful goddess and so has been used in the main diagrams given here.) Beyond the eastern wheel is a disk of emptiness, and another beyond the western wheel. (These were later interpreted as the elements of space and awareness, respectively.) All ten of these have curved knives as emblems. Also, draw many different emblems in the wind perimeter. (This is a brief reference to the perimeter beings; later Tibetan traditions of these are [[The perimeter beings of the Kālacakra maṇḍala|described here.)

The space perimeter is black. Further circles need to be drawn in this to create three bands: 3, 6 and 3 mus wide. The outer two of these are the actual space perimeter and the middle band is used to draw the green vajra-garland. The blazing light of the outer perimeter is of five colours (SG: and it swirls to the right, clock-wise).

2. Emblems of the deities

Mind palace

In the following notes, seed-characters from the Vimalaprabhā are given for completeness; the Vajrāvalī only lists the emblems. C: refers to the centre.

On the receptacle of the central lotus is a seat of stacked: white moon, red sun, black rāhu and red kālagni. On the lotus receptacle and its petals are:In the following notes, seed-characters from the Vimalaprabhā are given for completeness; the Vajrāvalī only lists the emblems. C: refers to the centre.

On the receptacle of the central lotus is a seat of stacked: white moon, red sun, black rāhu and red kālagni. On the lotus receptacle and its petals are:

C:	blue	huṃ	three-pointed vajra	Kālacakra	(dus kyi 'khor lo)
E:	black	a	censer	Kṛiṣṇadīptā	(nag mo 'bar ma)
SE:	black	ha	chowry	Dhūmā	(du ba ma)
S:	red	aḥ	lamp	Raktadīptā	(dmar mo 'bar ma)
SW:	red	haḥ	chowry	Marīcī	(smig rgyu ma)
W:	yellow	ā	conch	Pītadīptā	(ser mo 'bar ma)
NW:	yellow	hā	chowry	Pradīpā	(mar me ma)
N:	white	aṃ	divine food	Śvetadīptā	(dkar mo 'bar ma)
NE:	white	haṃ	chowry	Khadyotā	(me khyer ma)

Just outside the central lotus, in the corners formed by the inner beams of the tathāgata-dais, are four emblems:

SE: black wish-fulfilling jewel

SW: red dharma-semantron

NW: yellow wish-granting tree

NE: white dharma-conch

The next set of deities are the buddhas and their consorts, and they have between them a set of eight flasks. These are positioned right and left of the buddhas; there are also two further flasks, for above and below. These are placed in the east and west doorways, just beyond the lotuses for the wrathful deities.

The buddhas and their consorts are in the cardinal and intermediate directions of the tathāgata-dais, between the pillars. The lotuses in the cardinal directions are white with sun (red) seats, and those in the intermediate directions red with moon (white) seats:

Black Tārā with yellow Vairocana

E:	black	i	sword	Amoghasiddhi	(don yod grub pa)
SE:	black	ī	blue utpala	Tārā	(sgrol ma)
S:	red	ṛi	jewel	Ratnasambhava	(rin chen 'byung ldan)
SW:	red	ṛī	lotus	Pāṇḍarā	(gos dkar mo)
W:	yellow	ḷi	wheel	Vairocana	(rnam par snang mdzad)
NW:	yellow	ḷī	wheel	Buddhalocanā	(sangs rgyas spyan ma)
N:	white	u	lotus	Amitābha	(snang ba mtha' yas)
NE:	white	ū	utpala	Māmakī	(mā ma kī)

Next are the male bodhisattvas and their consorts, on the deity-podium of the mind palace. These all are on white lotuses with sun seats except the two left of west (L of W) and left of north which are on red lotuses and moon seats:

White Lokeśvara and red Rasavajrā

L of E:	blue	aṃ	vajra	Samantabhadra	(kun tu bzang po)
R of E:	black	e	sword	Khagarbha	(nam mkha'i snying po)
SE:	black	ai	cloth	Sparśavajrā	(reg bya rdo rje ma)
L of S:	green	a	vajra	Vajrapāṇi	(phyag na rdo rje)
R of S:	red	ar	jewel	Kṣitigarbha	(sa'i snying po)
SW:	red	ār	bowl of supreme flavour	Rasavajrā	(ro rdo rje ma)
L of W:	green	ā	dharmodaya	Dharmadhātuvajrā	(chos khams rdo rje ma)
R of W:	yellow	al	wheel	Nīvaraṇaviṣkambhin	(sgrib pa rnam sel)
NW:	yellow	āl	conch of perfume	Gandhavajrā	(dri rdo rje ma)
L of N:	blue	aḥ	vīna	Śabdavajrā	(sgra rdo rje ma)
R of N:	white	o	lotus	Lokeśvara	(jig rten dbang phyug)
NE:	white	au	mirror	Rūpavajrā	(gzugs rdo rje ma)

Next are the wrathful deities in the doorways of the mind palace. In the east and north these are on white lotuses and sun seats; in the south and west on red lotuses and moon disks:

White Padmāntaka (Mānaka) and Jambhakī

E:	black	yaṃ	sword	Atibala	(shin tu stobs)
S:	red	raṃ	club	Jambhaka	(rmongs byed)
W:	yellow	laṃ	hammer	Stambhaka	(rengs byed)
N:	white	vaṃ	lotus	Mānaka	(nga rgyal byed)

The available editions of the Vajrāvalī have these last two emblems the other way around, with lotus in the west and hammer in the north. This seems to be a mistake. (SG: There is an extra lotus in the eastern doorway for a fifth wrathful.)

Finally, for the mind palace, there are the offering goddesses on the plinth:

L of E:	black	cchjjhña	conch (containing perfume)	Gandhā	(dri chab ma)
R of E:	black	cchjjhñā	garland of blue flowers	Mālā	(phreng ba ma)
L of S:	red	ṭṭhḍḍhṇa	bowl of incense	Dhūpā	(bdug spos ma)
R of S:	red	ṭṭhḍḍhṇā	lamp	Dīpā	(mar me ma)
L of W:	yellow	tthddhna	head ornament	Lāsyā	(sgeg mo)
R of W:	yellow	tthddhnā	jewelled necklace	Hāsyā	(bzhad ma)
L of N:	white	pphbbhma	(bowl of) fruit	Amṛitā	(bdud rtsi ma)
R of N:	white	pphbbhmā	bowl of nectar	Halā	(bdud rtsi'i 'bras bu ma)

And, in the central cell of each toran in the mind palace:

E toran:	green	kkhgghṅā	cloth	Nṛityā	(gar ma)
S toran:	blue	sḥpṣśḥkā	lotus	Kāmā	('dod pa ma)
W toran:	green	kkhgghṅa	drum	Vādyā	(sgra ma)
N toran:	blue	sḥpṣśḥka	vajra	Gītā	(glu ma)

(SG: Describes using just golden drawing rather than lañca characters to represent these.)

Abhaya adds that the bowls in the north are both skulls and that the west toran drum is a paṭaha, a traditional Indian kettle-drum, a type usually used for proclaiming some event.

The seed-characters are considered to be stacked. For example, with cchjjhña, the character ca is on top, below it cha, then ja, jha, and finally ña on the bottom. The green and blue goddesses are to be drawn in the middle cells of the upper stages of the torans of the mind palace.

Speech palace

This completes the deities of the mind palace, and we now come to the deities on the eight lotuses in the speech palace. On each lotus there is a male and female deity (with the female the chief, facing the centre of the maṇḍala), surrounded by eight yoginīs. On the podium in both the speech and body palaces, the lotuses in the cardinal directions are red and in the intermediate directions, white. They have neither moon nor sun seats. Instead, they each have an animal mount, which in this tradition is drawn underneath the lotus. The same applies to the lotuses of the body palace podium.

In the following, the petals are numbered from the eastern-most petal, clockwise. The animal mounts under the lotuses are given in brackets. (There are many different names here from the equivalent list given in the Vimalaprabhā.)

East (red preta):

C:	black	ha	curved knife	Carcikā	(tsar tsi ka)
1:	black	hi	curved knife	Bhīmā	(jigs byed ma)
2:	black	ya	curved knife	Ugrā	(drag mo)
3:	black	yi	curved knife	Kāladaṃṣṭrā	(mche ba nag mo)
4:	black	yṛi	curved knife	Jvalanmukhā	(kha nas me 'bar ba)
5:	black	hī	curved knife	Vāyuvegā	(rlung shugs ma)
6:	black	yu	curved knife	Pracaṇḍā	(rab gtum ma)
7:	black	yḷi	curved knife	Raudrākṣī	(drag mig ma)
8:	black	yaṃ	curved knife	Sthūlanāsā	(sna sbom mo)

South-east (garuḍa):

C:	black	kṣa	wheel	Vaiṣṇavī	(khyab 'jug ma)
1:	black	kṣi	wheel	Śrī	(dpal mo)
2:	black	yā	wheel	Māyā	(sgyu ma mo)
3:	black	yī	wheel	Kīrtti	(grags ma)
4:	black	yṛī	wheel	Lakṣmī	(phun sum tshogs ma)
5:	black	kṣī	wheel	Vijayā	(rnam par rgyal ma)
6:	black	yū	wheel	Śrījayā	(dpal ldan ma)
7:	black	yḷī	wheel	Śrījayantī	(dpal ldan rgyal byed ma)
8:	black	yaḥ	wheel	Śrīcakrī	(dpal 'khor lo ma)

South (buffalo):

C:	red	haḥ	club	Vārāhī	(phag mo)
1:	red	hṛi	club	Kaṅkālī	(keng rus ma)
2:	red	ra	club	Kālaratri	(dus mtshan ma)
3:	red	ri	club	Prakupitavadanā	(rab tu khros gdong ma)
4:	red	rṛi	club	Kālajihvā	(dus kyi lce ma)
5:	red	hṛī	club	Karālī	(gtsigs ma)
6:	red	ru	club	Kālī	(nag mo)
7:	red	rḷi	club	Ghorā	('jigs ma)
8:	red	raṃ	club	Virūpā	(gzugs ngan ma)

South-west (peacock):

C:	red	kṣaḥ	spear	Kaumārī	(gzhon nu ma)
1:	red	kṣṛi	spear	Padmā	(padma ma)
2:	red	rā	spear	Anaṅgā	(yan lag med ma)
3:	red	rī	spear	Kaumārī	(gzhon nu ma)
4:	red	rṛī	spear	Mṛigapatigamanā	(rigs kyi bdag po'i 'gros ma)
5:	red	kṣṛī	spear	Ratnamālā	(rin chen 'phreng ba ma)
6:	red	rū	spear	Sunetrā	(shin tu spyan ma)
7:	red	rḷī	spear	Līnā	(sdug ma)
8:	red	raḥ	spear	Subhadrā	(bzang mo)

West (Airāvata, elephant):

C:	yellow	hā	vajra	Aindrī	(dbang mo)
1:	yellow	hḷi	vajra	Vajrābhā	(rdo rje 'od ma)
2:	yellow	la	vajra	Vajragātrā	(rdo rjei lus can ma)
3:	yellow	li	vajra	Kanakāvatī	(gser ldan ma)
4:	yellow	lṛi	vajra	Urvaśī	(las dbang ma)
5:	yellow	hḷī	vajra	Citralekhā	(ri mo sna tshogs ma)
6:	yellow	lu	vajra	Rambhā	(chu shing ma)
7:	yellow	lḷi	vajra	Ahalyā	(a nya lags ??)
8:	yellow	laṃ	vajra	Sutārā	(shin tu mig 'bras ma)

North-west (goose):

C:	yellow	kṣā	mace	Brahmāṇī	(tshangs pa ma)
1:	yellow	kṣḷi	mace	Sāvitrī	(mchod sbyin 'don ma)
2:	yellow	lā	mace	Padmanetrā	(padma can)
3:	yellow	lī	mace	Jaladavatī	(chu skyes can ma)
4:	yellow	lṛī	mace	Buddhi	(blo ma)
5:	yellow	kṣḷī	mace	Vāgīśvarī	(ngag gi dbang phyug ma)
6:	yellow	lū	mace	Gāyatrī	(glu mkhan ma)
7:	yellow	lḷī	mace	Vidyut	(glog ma)
8:	yellow	laḥ	mace	Smṛiti	(dran ma)

The term mace is used here to indicate the pointed club of Brahma.

North (bull):

C:	white	haṃ	trident	Raudrī	(drag mo)
1:	white	hu	trident	Gaurī	(gau rī)
2:	white	va	trident	Gaṅgā	(gaṃ gā ma)
3:	white	vi	trident	Nītyā	(gtum ma)
4:	white	vṛi	trident	Tvaritā	(myur ma)
5:	white	hū	trident	Totalā	('debs ma)
6:	white	vu	trident	Lakṣaṇā	(mtshan nyid ma)
7:	white	vḷi	trident	Piṅgalā	(dmar ser ma)
8:	white	vaṃ	trident	Kṛiṣṇā	(nag mo)

North-east (lion):

C:	white	kṣaṃ	lotus	Lakṣmī	(phun sum tshogs ma)
1:	white	kṣu	lotus	Śrīśvetā	(dpal ldan dkar mo)
2:	white	vā	lotus	Candralekhā	(zla ba'i ri mo can ma)
3:	white	vī	lotus	Śaśadharavadanā	(ri bong 'dzin zhal ma)
4:	white	vṛī	lotus	Haṃsavarṇā	(ngang pa'i mdog ma)
5:	white	kṣū	lotus	Dhṛiti	('dzin ma)
6:	white	vū	lotus	Padmeśā	(padma'i dbang mo)
7:	white	vḷī	lotus	Tāranetrā	(skar mig ma)
8:	white	vaḥ	lotus	Vimalaśaśadharā	(dri med ri bong 'dzin ma)

(SG: Only gives the animals for the intermediate directions, presumably because the animals cannot be drawn for the cardinal directions as the lotuses are in the central cells of the mind toran. The fact that Abhaya gives these animals perhaps suggests the method of the Vimalaprabhā, in which the animals are on top of the lotus receptacles.)

Body palace and beyond

Next are the deities of the body palace podium. There are 12 lotuses on the podium, each with 28 petals. On the receptacle of each lotus there is a male and female deity (this time the male is the chief deity), surrounded by twenty-eight yoginīs.

The ordering of the lotus petals is quite different from the lotuses in the speech palace, and the structure of the list of characters from which these deities arise is also different. There are 30 deities in each group, and their seed-characters are a combination of a group of five consonants with six vowels. For example, on the lotus right of the eastern door, the set of consonants is: ca, cha, ja, jha and ña. These are combined in reverse order with the vowels: a, i, ṛi, u, ḷi and aṃ. This produces the following list of 30 characters:

ña, ñi, ñṛi, ñu, ñḷi, ñaṃ, jha, jhi, jhṛi, jhu, jhḷi, jhaṃ, ja, ji, jṛi, ju, jḷi, jaṃ, cha, chi, chṛi, chu, chḷi, chaṃ, ca, ci, cṛi, cu, cḷi, caṃ.

These represent the 30 lunar days of the month of Caitra, and the deities for the 15th (full Moon) and 30th (new Moon) lunar days, are respectively the female and male deities on the receptacle of the lotus. Their characters are jṛi and caṃ. The remaining 28 characters are placed sequentially on the petals of the lotus, but exactly how is not described clearly in the original literature.

It is usually accepted that the characters are placed in order, first on the eastern petal of the inner ring of four petals, then proceeding clockwise, moving to the eastern petal of the middle ring after the inner is complete, and so on. The characters are placed in the order given above, with dzṛi and tsaṃ omitted as their deities are on the receptacle.

Moving around the podium clockwise, the next lotus is in the south-east, and the vowels are now long, and combined with the same consonants, but in the normal order:

cā, cī, cṛī, cū, cḷī, caḥ, chā, chī, chṛī, chū, chḷī, chaḥ, jā, jī, jṛī, jū, jḷī, jaḥ, jhā, jhī, jhṛī, jhū, jhḷī, jhaḥ, ñā, ñī, ñṛī, ñū, ñḷī, ñaḥ.

As before, jṛī and ñaḥ are omitted from the group when placing them on the petals.

For all twelve lotuses:

Nairṛiti

L of E:	black	ka kha ga gha ṅa	wheel	Viṣṇu	(khyab 'jug)
R of E:	black	ca cha ja jha ña	sword	Nairṛiti	(bden bral)
SE:	black	ca cha ja jha ña	wishing tree	Vāyu	(rlung lha)
L of S:	red	ka kha ga gha ṅa	vajra-club	Yama	(gshin rje)
R of S:	red	ṭa ṭha ḍa ḍha ṇa	lance	Agni	(me lha)
SW:	red	ṭa ṭha ḍa ḍha ṇa	spear	Ṣaṇmukha	(gdong drug)
L of W:	yellow	sa ḥpa ṣa śa ḥka	jewel or mace	Kubera	(lus ngan po)
R of W:	yellow	ta tha da dha na	vajra	Śakra	(dbang po)
NW:	yellow	ta tha da dha na	needle	Brahmā	(tshangs pa)
L of N:	white	sa ḥpa ṣa śa ḥka	trident	Rudra	(drag po)
R of N:	white	pa pha ba bha ma	fetter	Samudra	(rgya mtsho)
NE:	white	pa pha ba bha ma	axe	Gaṇeśa	(tshogs bdag)

Left of west, instead of "jewel or mace" as the text states, we should probably read a jewel-tipped mace. In traditions for the Kālacakra maṇḍala other than the Vajrāvalī, the deities LoE and LoS are green and those LoW and LoN blue. The fact that they are here the colours of their directions is one of the most prominent differences with the Vajrāvalī, and identification of this feature is the easiest way to recognise a maṇḍala from Abhayākaragupta's tradition.

The mounts are:

L of E: garuḍa (SG: red)

R of E: red preta (SG: flesh coloured)

SE: deer (SG: yellow )

L of S: buffalo (SG: blue)

R of S: sheep

SW: peacock

L of W: elephant

R of W: elephant

NW: goose

L of N: bull (SG: blue)

R of N: sea-monster (makara, chu srin) (SG: red)

NE: mouse (SG: blue)

Next are the wrathful deities in the doorways of the body palace, plus one above and one below, each drawn by seven draught animals. At this point, Abhaya states that the emblems are placed on lotuses. Four chariots were described earlier for these deities, and the lotuses will be on the chariots, but what about the other two? He states that the other two emblems are just beyond those in the eastern and western doorways. There is not much space to draw them that way, and so some draw the chariots side by side, while others have the above and below chariots beyond the tops of the eastern and western torans. The latter method seems the most accepted.

The wrathful Acala

East door:	black	ya	club	Nīladaṇḍa	(dbyug pa sngon po)
South door:	red	ra	arrow	Ṭakkirāja	('dod pa'i rgyal po)
West door:	yellow	la	mace	Mahābala	(stobs po che)
North door:	white	va	pestle	Acala	(mi g.yo ba)
Above:	green	haṃ	vajra	Uṣṇīṣacakravartī	(gtsug tor 'khor los sgyur ba)
Below:	blue	ha	trident	Sumbharāja	(gnod mdzes rgyal po)

The draught animals pulling these chariots are:

E: boars

S: horses

W: elephants

N: lions

A: three-eyed, five-coloured garuḍas

B: eight-legged lions (śarabha)

The final list of emblems described in the Vajrāvalī are for a group of thirty-six goddesses ('dod ma, icchās) on the plinth of the speech palace, and an equivalent group of thirty-six goddesses (phyir 'dod ma/mi 'dod ma, pratīcchās) on the plinth of the body palace.

Their colours, hand emblems, directions, etc., all match between the two groups, and their seeds are easily converted between the two. For example the seed of Vidveṣecchā on the speech plinth is caḥ, and of the equivalent Vidveṣapratīcchā on the body plinth is caṃ.

It is with this list of goddesses that one finds the greatest variations between the different texts and traditions, in the spelling of their names, their emblems, their positions and their physical descriptions. There is no such thing as a definitive list of these goddesses.

The icchā goddesses are associated with groups of other goddesses in the maṇḍala: four buddha consorts, six bodhisattva consorts, four mind palace wrathfuls' consorts, the eight chief goddesses of the speech palace, the six wrathfuls' consorts on chariots, and, the eight pracaṇḍā. They are also associated with another group of 36 mātṛikā goddesses in the maṇḍala of 100 yoginīs, which are themselves connected to the 36 professional castes in medieval Bengal. The list is given here for the icchās of the speech palace. They are described in eight groups, those to the right and to the left of the doorway, the one nearest to the doorway first. In the groups of five to the right of each doorway, the last in each list are considered by some to be on the corners of plinth.

RoE (all black):

utpala	Vidveṣecchā	(zhe sdang 'dod ma)
clothing	Amśukecchā	(gos 'dod ma)
curved knife	Kāyakaṇḍūyanecchā	(lus 'phrug 'dod ma)
wheel	Vadanagatakaphotsarjanecchā	(kha lud 'dor 'dod ma)
khaṭvāṅga	Uccāṭanecchā	(skrod 'dod ma)

LoE (all black, except one):

curved knife	Saṃtāpecchā	(rab tu chab 'dod ma) (blue)
sword	Sparśecchā	(reg bya 'dod ma)
curved knife	Sarvāṅgakṣepaṇecchā	(yan lag thams cad dkrug 'dod ma)
curved knife	Utsṛiṣṭabhaktecchā	(lhag ma za 'dod ma)

RoS (all red):

lotus	Stobhanecchā	(bstod par 'dod ma)
bowl of food	Bhojanecchā	(zas 'dod ma)
club	Aṅgamalecchā	(yan lag gi sku mnyed 'dod ma)
spear	Nṛityecchā	(gar 'dod ma)
lotus	Śoṣaṇecchā	(skam 'dod ma)

LoS (all red, except one):

arrow	Ākṛiṣṭīcchā	(logs su 'gugs 'dod ma)
axe	Dhāvanecchā	(rgyug 'dod ma) (green)
curved knife	Mūtraviṭśamanecchā	(dri chen dri chu spong 'dod ma)
curved knife	Saṃgrāmecchā	(g.yul ngo 'dod ma)

RoW (all yellow):

wheel	Stambhanecchā	(rengs 'dod ma)
perfume conch	Gandhecchā	(dri chab 'dod ma)
vajra	Śayanecchā	(nyal 'dod ma)
needle	Peyapiplāvanecchē	(chul 'dzul 'dod ma)
wheel	Bandhanecchā	(bcings 'dod ma)

LoW (all yellow, except one):

dharmodaya	Maithunecchā	('khrig pa 'dod ma) (green)
wheel	Kīlanecchā	(phur bu 'debs 'dod ma)
curved knife	Vajranecchā	(slu 'dod ma)
curved knife	Ahibandhanecchā	(sbrul gyis bcings 'dod ma)

RoN (all white ):

utpala	Puṣṭīcchā	(rgyas 'dod ma)
mirror	Bhūṣaṇecchā	(rgyan 'dod ma)
trident	Āsanecchā	(gdan 'dod ma)
lotus	Rajyecchā	(rgyal po'i srid 'dod ma)
utpala	Mṛiduvacanecchā	('jam par smra 'dod ma)

LoN (all white, except one):

vīṇā	Vādyecchā	(sgra 'dod ma) (blue)
hammer	Bandhanecchā	(phyag 'tshal 'dod ma)
curved knife	Bahukalahecchā	(thab mo mang po 'dod ma)
curved knife	Dārakakrīḍanecchā	(khye'u la khro 'dod ma)

(SG: Suggests that the emblems are not drawn, but lañca characters instead.)

Abhaya does not at this point mention emblems for the nāgas or the pracaṇḍas – these were described earlier. For the sake of completeness, their names and seeds are given here:

Nāgas:

The yellow nāga Takṣaka with black Kākāsyā

L of E:	black	hya	victory banner	Karkkoṭa	(stobs kyi rgyu)
R of E:	black	hyā	victory banner	Padma	(padma)
L of S:	red	hra	svastika	Vāsuki	(nor rgyas)
R of S:	red	hrā	svastika	Śaṅkhapāla	(dung skyong)
L of W:	yellow	hla	vajra	Takṣaka	('jog po)
R of W:	yellow	hlā	vajra	Mahāpadma	(padma chen po)
L of N:	white	hva	lotus	Ananta	(mtha' yas)
R of N:	white	hvā	lotus	Kulika	(rigs ldan)
Above:	green	huṃ	flask	Jaya	(rgyal ba)
Below:	blue	kṣuṃ	flask	Vijaya	(rnam par rgyal ba)

Pracaṇḍās (all emblems are curved knives):

The pracaṇḍā Jambukāsyā

E:	black	kkhgghṅa	Śvānāsyā	(khyi gdong ma)
SE:	black	cchjjhña	Kākāsyā	(khwa gdong ma)
S:	red	lvrykṣa	Śūkarāsyā	(phag gdong ma)
SW:	red	ṭṭhḍḍhṇa	Gṛidhrāsyā	(bya rgod gdong ma)
W:	yellow	sḥpṣśḥka	Jambukāsyā	(ce spyang gdong ma)
NW:	yellow	tthddhna	Garuḍāsyā	(mkha' lding gdong ma)
N:	white	lvryha	Vyāghrāsyā	(stag gdong ma)
NE:	white	pphbbhma	Ulūkāsyā	('ug gdong ma)
A:	green	ha	Anīlā	(sngon mo)
B:	blue	haḥ	Vajrākṣī	(rdo rje mig can ma)

In the Vajrāvalī's companion text, the Niṣpannayogāvalī (rdzogs pa'i rnal 'byor gyi phreng ba), Abhaya has these last two on chariots, rather than the disks of emptiness as described earlier. (SG: Has here two wheels in both the east and west; they all have eight-petalled lotuses on their hubs, and have no animal seats.)

If the animal mounts are drawn underneath the wheels, they are:

E: rhinoceros

SE: bheruṇḍa (a yellow bird)

S: bear

SW: crane

W: lion

NW: nīlākṣa, (a blue bird)

N: yak

NE: bat

The final emblems that need to be mentioned are those of the perimeter beings in the perimeter of wind (or more usually on the border between the wind and fire perimeters). These are not given in the Vajrāvalī but are mentioned in the Niṣpannayogāvalī. This first gives the position of the planets, each on disks of elements. It simply names them, without giving any emblems or seeds.

E: wind – Moon

SE: wind – Sun

S: fire – Mercury

SW: fire – Mars

W: earth – comet (mjug rings)

NW: earth – Saturn

N: water – Venus

NE: water – Jupiter

A: space – Rāhu (sgra gcan, Moon's ascending node)

B: space – Kālāgni (dus me, descending node)

The text then simply names some of the other perimeter beings: Dhruva (the Pole Star), Agastya (presumably Canopus), the 28 lunar mansions, the 12 signs of the zodiac, the 16 phases (of the Moon), the worldy protectors of the 10 directions, Nandi (dgaa can), Mahākāla (nag po chen po), Ghaṇṭākarṇa (dril bu'i rna ba can), Hāriti ('phrog ma), Bhṛṅgī (nyam chung), and large numbers of field protectors (kṣetrapāla, zhing skyong), messengers (dūtī, pho nya), and siddhas (grub pa).

No particular instructions are given, and so an artist would represent as many of these as seems appropriate, with different colours, emblems, and so forth. However, two traditions have been developed in Tibet for these beings to be represented by specific seed-characters between the charnel grounds - a total of 88 developed by Buton, used for example in the Gelug tradition, and a total of 112 used in the Karma Kagyu tradition. These traditions are both described on this web page.

This completes the decription of the Kālacakra maṇḍala from the Vajrāvalī.

Source

kalacakra.org