In this essay I will present continuity of historical artifacts of the geometrical symbol that is known as the “Flower of Life” in modern day. Origins of the symbol dates at least to the beginning of the 2nd millenium BC in Mesopotamia. Intermediate knowledge of the ancient Near East and western history of mathematics is required from the reader as well as elementary knowledge of art, geometry and religions. Reader is also expected to know basics of the Flower of Life geometry. I hope document will provide key sources for investigators willing to do further research with the topic.
Reflections after the research trip
I made a six week research trip to Greece, Turkey, France and Sweden in summer 2014. Since that I’ve been systematically collecting pictures of artifacts that have the Flower of Life symbol (later called by the abbreviation FOL) printed, carved or some way presented on them. Few websites already had a good collection of the occurrences. However, I think my personal findings on archaeological sites and museums following exhausting research on the Internet has brought up new, interesting facts that are not really collected in this form anywhere else before.
Flower of Life Wiki page (in August 2014) assumes that one of the earliest occurrences of the FOL is in an Assyrian carpet stone dated at around 650 BC. The Wiki page also questions the dating of the FOL that is imprinted on the Osirian temple stone in Abydos. This occurrence was first reported by the New Age author Drunvalo Melchizedek in his lectures in 1980’s and 1990’s and later officially in his two volume book “The Ancient Secret of the Flower of Life”. Drunvalo is also responsible of the term “Flower of Life” (not to be confused with Fleur de lis or Tree of Life) that is used to describe this particular geometrical figure. Due to his background in New Age philosophy, many topics surrounding the FOL are highly controversial. While dating of the FOL in Abydos is debated, it is evident that the symbol was known quite widely already in 1600 – 1400 BC. We have objects from that time which show clearly the same or similar decoration. These objects originate in Egypt Thebes [item 2], Northern Iran Marlik [item 3], Greece Mycenae [item 1] and Cyprus [item 5].
Theorizing the origins
Mathematical practice relating to intersecting circles can be seen from Babylonian clay tablets in 2100 – 1600 BC, although not presenting exactly the figure of the FOL. Eleanor Robson shows onher book the image of the four petal rosette or conclave square which ancient Babylonians called Apsamikkum that can be rendered as Cow’s Nose or Sound hole of the lyre. Ceremonial vessel from Indus Valley Harappa civilization 2600 – 2450 BC and others from Harappa and Mohenjo-daro indicates that this particular symbol was known in the Indus Valley already in 3000 BC. But because desing was known “from Halaf pottery of the sixth millennium BC to images of Neo-Assyrian textile” (The apsamikku in Neo-Babylonian Mathematics page 214) in the Syria, it is quite certain that Cow’s Nose symbol came somewhere from the ancient Fertile Crescent.Cow’s nose (apsamikkum) -pattern
Flower of Life
The FOL symbol instead is basically produced by six intersecting circles around the seventh central circle forming a hexagon on the crossing points. It is even easier to draw with a plain drafting compass or dividers than Cow’s Nose since you continue forming the pattern only from the crossing points. In Cow’s Nose pattern you need to find straight lines and right angles as well. This can be verified by doing both figures manually. Below is a computer generated version of the Flower of Life pattern.Flower of Life -pattern
Outside of the scope of the essay, but intriguingly enough: if sound holes of the lyre or harp are called apsamikkum like Lawergren & Gurney in the Sound Holes And Geometrical Figures points, actual shapes of the holes resemble more like equilateral triangles of the FOL than concave squares or rectangles in some cases. It could rather be that apsamikkum refers to the hole, window and frame of the figure, not the exact shape of it. If the FOL symbol had any particular name for ancients, I leave it for future speculations.
Practice from clay tablets (IM 52916, Susu, MS 3051 on “A Remarkable Collection of Babylonian Mathematical Texts” by in Joran Friberg, page 207) shows equilateral triangle and hexagon calculations with the square root of 3 approximations. These arithmetic and geometric properties are fundamental in the FOL. In addition, sexagecimal place value system was already known in the 3rd millenium BC. Geometrical link between circle, hexagon and sexagecimal system is genuinely demonstrated by Jaime Vladimir. Yet the Sumerian brown stone cylinder seal with two six-petal rosettes originates from 3000 BC. Actually similar seals can repeatedly be found from the late Uruk and Jemdet Nasr period ie. 3100 – 2900 BC.
The pillar cone mosaic from the ancient Sumerian city, Uruk in 3400 – 3100 BC, shows a tessellation pattern in the temple pillars. 60 degrees zig-zag rhombus or lozenge pattern formed from two equilateral triangles is inside the FOL geometry. Those who want to go deeper to the triangle study should read “Mysteries of the equilateral triangle” by B.J. McCartin.
We can pretty safely conclude that already in the beginning of the 2nd millenium BC people on ancient Mesopotamia were playing with construction elements and pattern we find in the FOL. On the other hand, conclusion based strictly on artifacts is that four (or eight) pointed flowers and rosettes were more prominent and only later six pointed stars and petals came for decoration motifs and deeper mathematical interest. Still, Assyrian ornament [item 33] in the museum of Pergamo can stretch the origin of the FOL further, even to 3000 BC, if my request to the museum to give more information about the ornaments gets any attention and dating can be confirmed.
Early visible traces
Most of the artifacts from 1400 BC to 500 BC are found from an area that is nowadays Syria, Iraq and Iran. Political situation, illegal trade of the antiquities that has been continuing for the last two hundred years, immature web technologies on museum websites and many other things in Near East makes the whole FOL topic really hard subject to research. There are just a few scholarly works that refer to the FOL, often with an association to the six-petal rosette figure. Anyway, at some point this geometrical motif arrived from mainland to Cyprus (being a cult site of Aphrodite), Samos and Miletos (both being birthplaces of famous mathematicians, namely Pythagoras and Thales). This can be read from the history of theGreek vases (pages 47-57) by B.B. Shefton:
“…it presents us with a rosette motif that, while it is not often found in Greek art, has a story to it of considerable interest, one that has only partially been explored by previous investigators… the net pattern first half of ninth century BC … from Samaria are the earliest ones known to me, if indeed their early date can still be maintained… Earliest occurrence known to me is on the underside of a Middle Geometric Attic pyxis from the Kerameikos, that is to say some time in the second quarter of the eighth century…”
Greeks, however, didn’t use the motif in its full extent, but were mostly interested in its six-petal rosette form. It is still notable that golden plates having a six-petal rosette decoration comes from Greece Mycenae [item 1] as early as 1600 BC and an ivory whorl [item 5] from Cyprus (1300 – 1100 BC) which Shefton didn’t mention. Shefton also didn’t mention anything about earlier dating goblets from Marlik [item 3] or about a wooden lid from Egypt [item 2].
Phoenicians in Nimrud around 700 BC decorated ivory items like pyxis [item 8], elephant tusk [item 10] and plaque [item 11] with the FOL symbol. Use of the symbol is very natural as they stayed right in the center of Levant, ie. half way from Egyptian kingdom to Mesopotamia, where all major trade of goods, skills and knowledge was made for thousands of years. Stone door sills [item 13] having a decoration drawn with a compass and giving the effect of flowers with six petals (continuous FOL pattern) are from King Ashurbanipal temple in Nineveh, 645 BC. Assyrian Carpets in Stone by Pauline Albenda (1978) lists several similar stone carpets from Nimrud, but also she seems to be unaware of Marlik culture goblets or Egyptian existence of the ornament.
Oldest instance of the FOL that I have found in the Asia is from Maharashtra, India, 200 – 100 BC [item 16]. It is an arch decoration from the Buddhist Bedse caves. It is also mentioned that decoration motifs around the cave is similar to Greco-Assyrian style. Newer instances comprise of Chinese Lion-Dog sculptures [item 34] and a marble floor decoration in a Sikh temple [item 35].
At the dawn of the Common Era
One interesting thing is that the FOL symbol was extensively used by Jews, Greeks and Romans around the dawn of the new era, 100 BC – 200 AD [item 17, 18, 19, 20 and 21]. Especially mosaic floors pop up from the history using this theme often next to the Cow’s Nose decoration motif. Decorations in the temples of Herod and the religious center of Ephesus are one of the most beautiful and complete forms of the FOL. Intriguing question about the influence and usage of the symbol comes by its mathematical properties. This would warrant a separate article: were early Christians, Gnostics, middle Platonists and Neopythagoreans aware of the FOL? How about writers of the Gospels and the book of Revelation, did they know the meaning of it? Without going any deeper into the subject, it must be mentioned that Roman imperium was spread up to Thrace in 180 AD leaving behind a few floor mosaics with the FOL symbol [item 24]. These can nowadays be witnessed in the excavated sites in Bulgaria, even in Spain [item 17 and 37] and France [item 23a and23b].
If I would really need to guess the origin of the geographical area, where the FOL was first used in its fullest magnitude, my bet would be on upper Mesopotamia. So rich is the tradition of using geometrical forms, especially usage of the six petal rosette and tradition has lasted long. Item 26 shows the painting of the wall (729 AD) in Syria desert which origin is highly interesting and urges deeper research. Wall is full of symbols of the FOL in different forms resembling figure settings in Abydos wall and on the other hand notes of Leonardo da Vinci.
1500 AC and still going strong
Much later geometrical patterns were used in the Arabic culture as an art itself. This is due to the fact that in their tradition God, prophets or even people and animals were not allowed to be drawn. For example, Ottomans used the FOL on cemetery works, sarcophagi and tombs [item 29a and 29b]. Orthodox christians in Patmos island applied geometry above the chapel door lunette [item31a and 31b], thus appreciating the symbology behind the intersecting circles. You can see more complex figure on the lunette only when zooming in to the image, which just adds tickling enigma around the symbol. Multicolor opaque glass “Cosmati” pavement in the Westminster Abbey Gothic church [item 27] has the symbol. It is well known that Vesica Piscis (ladder of a fish) is the basis of the FOL geometry and used widely on iconography though in the Orthodox tradition it is rather called a mandorla (almond) or a nimbus. The FOL tradition can easily go to the beginning of the Christian church and it can also be traced far to the history before that, as it is possible to see now.
At this point is is good to lift up once more the speciality of the symbol and at the same time its undiscovered history. Serçe Limani in his Shipwreck -book lists several lead net sinkers that has the six petal rosette symbol on them and writes:
“regardless of its purpose, the rosette, rare among the Jewish remains of Greece and Rome, is a particularly eastern Jewish phenomenon… rosettes, used as ornament details on fifth- and sixth century churches, were a particularly eastern Christian phenomenon as well, being peculiar to northern Syria.”
So simple is the formation that E.R. Goodenough, the author of the monumental thirteen-volume work about the Jewish and Christian symbolism calls it “the most banal of all designs” as quoted by Limani. Neither Goodenough and Limani knows hardly anything about the FOL in its full pattern, or its six petal rosette form from much much older history like golden plates in Mycenae [item 1].
Finally, my historic survey ends at around 1500 AD, when Leonardo da Vinci used several pages on his sketchbook [item 30] to investigate the properties of the hexagonal net / grid when he studied the theory of lunes (Wolfram Science, page 872, note d). He was interested in the proportions of such a grid which can be found from nature, for example bumble bee cells, turtle’s carapace and snowflakes. The theory of lunes, ie. geometric figures formed by the intersection of two circular arcs, was invented by the Greek mathematician Hippocrates of Chios in 440 BC. Both Leonardo and Hippocrates were doing this to unveil the ancient “squaring the circle” enigma, which also is a topic worth another article.
List of Flowers
I have collected the following list of the FOL artifacts and ordered them by time from the oldest to the newest, undated items to the end of the list. I hope this list will help further investigators to find out more details of the objects, their origin and history that could reveal more about the history of the FOL itself. On picture descriptions I will tell shortly where objects can be found, their dating and sometimes other additional notes, links and references. It is very probable that more objects will be found in future. Think approximately half a million clay tablets that has been excavated from the Near East so far. Reading, cataloging and interpreting them is still considered to be in child steps. Many times more tablets are supposed to hide under the ground. Same applies to treasures in Egypt. Maybe thousands of relating objects are in private collections around the world waiting to see the daylight in uncertain future. Many, maybe most of the museums doesn’t have online picture collections of the objects. So only when individuals and researchers has this particular subject on their mind, they may pay attention to the FOL geometry in the artifacts. For example the goblet in the Medelhavsmuseet in Stockholm [item 14] was found only, when I realised week earlier that the FOL can be seen from the bottom or underside of the object. So when I saw attracting silver object in the museum glass vitrine, my first thing to do was to peek inside it. It was truly amazing to see the perfect FOL appearing there right under my eyes.
2000 – 0 BC
Golden rosettes [item 1]
Golden six-petal rosettes in the archaeological museum of Istanbul. Mycenae, Greece, 1600 BC. (Photo credit: Marko Manninen)
Cosmetic box [item 2]
A circular wooden cosmetic box with a swivel lid in the The Metropolitan Museum of Art in New York. Thebes, Egypt, 1492 – 1473 BC. Note resembling 12 petal rosette in the ivory box 1550 BC and 32 ray straight line star from the same period. (Photo credit: MET)
Silver goblet [item 3]
A silver goblet in the museum of Louvre. Underside of the object was unreachable for the visitors because the goblet stands on thick basement. But picture in the object description shows a full Flower of Life pattern in the bottom, very much similar to the silver goblet underside decoration in Stockholm [item 14]. Unfortunately only very little is known about the Marlik culture, but artifacts found from the royal cemetery shows excellence in the gold and silver metalwork. Marlik, northern Iran, 1400 – 1100 BC. (Photo credit: Marko Manninen)
Golden goblet [item 4]
Underside of a golden goblet in the museum of Louvre. Excavation report shows several artifacts having similar six-petal rosettes with surrounding petals under the goblets and beakers. Marlik, Iran, 1400 – 1100 BC. (Photo credit: © 1985 Photo RMN / Pierre et Maurice Chuzeville)
Ivory whorl [item 5]
An ivory whorl as seen in the British Museum. Cyprus, Greece, 1340 – 1050 BC. Note how peripheral petals are roughly made probably by a hand. This is a good example how precise much work it takes to draw the whole FOL pattern after the first seven simple circles.
Phoenician bowl [item 6]
A phoenician bowl in the Los Angeles County Museum of Art. 850 BC.
Idalion cup [item 7]
A cup with mythological scenes and flower of life pattern in the in its center visible in the Louvre museum. Idalion, Cyprus, 800 – 700 BC. (Photo credit: Public Domain)
Oval pyxis [item 8]
An oval pyxis with a base and a lid in the Iraq Museum, Baghdad. Nimrud, 800 – 700 BC. Note the object IM79513 that has similar, but badly cracked lid with the same geometric figure. (Photo source & credit: G. Herrmann & S. Laidlaw: Ivories from Nimrud VI)
Terracotta torso [item 9]
A cypriot terracotta torso in the British Museum. Salamis, Greece, 700 BC. (Photo source & credit: B.B. Shefton: Greek vases)
Ivory tusk [item 10]
A carved ivory tusk in the Iraq Museum, Baghdad. Nimrud, 800 – 700 BC. (Photo source & credit: G. Herrmann & S. Laidlaw: Ivories from Nimrud VI)
Ivory plague [item 11]
A fragment of an ivory plaque in the Iraq Museum, Baghdad. Nimrud, 800 – 700 BC. (Photo source & credit: G. Herrmann & S. Laidlaw: Ivories from Nimrud VI)
Bronze vessel [item 12]
A bronze vessel from the palace of Sennacherib. New York public library. Iraq, Nimrud, 700 BC. (Photo source & credit: NYPL Digital Library)
Stone floor sill [item 13]
A stone floor sill with a field of interlocking circles decoration from the palace of King Ashurbanipal. Visible in the Museum of Louvre. Related objects are also visible in the British Museum (BM 118910, BM 118913). The northern Iraq, 645 BC. (Photo credit: Marko Manninen)
Silver beaker [item 14]
An ancient Near East silver beaker bottom motif 600 – 500 BC. Object is in the Swedish Medelhavsmuseet. Kind staff from the museum also gave me this information: “The archived accession catalogue gives that it was received in 1980, probably through a certain O. Engkvist. There is also a comment in the margin: Prob Archaemenid, acc. To Vincent Pigott (Iran in the Near East), Prof pennsylvania, USA. Personal communication”. (Photo credit: Ove Kaneberg)
Ornament at the Temple of Osiris [item 15]
An ornament found at the stone slab in the Temple of Osiris. Claimed to have origins from 3000 BC (or even much older), but critical analysis gives dates from 400 BC – 200 BC to even after 1900 AD. Abydos, Egypt. (Photo credit: Ray Flowers)
Cave arches [item 16]
Chaitya arches in form of wood lattice patterns, floral patterns, berm-rail arches and a parapet with Assyrian pattern of a row of stepped triangles in the Buddhist temple of Pitalkhora. Maharashtra, India, 200 – 100 BC. (Photo credit: Vivek S. Kale)
Opus signinum [item 17]
Opus signinum (mosaic floor) of the Roman period house in the “city of charity”, Caminreal. Spain, 200 BC – 100 BC. (Photo source and credit:Jalme D.V. Redon)
Floor mosaic at Ephesus [item 18]
Floor mosaic that lays on the house 1a on the Curetes Street, near the Library of Celsus in the archaeological site of Ephesus, Turkey, 100 BC. (Photo credit: Ken & Nyetta)
Floor mosaic in Cyprus [item 19]
Mosaic floor ornament of late Hellenistic period at Roman agora, the archaeological site of Kourion in Cyprus. 75 – 50 BC. (Photo credit: Andrew Sweeney)
Floor mosaic [item 20]
Floor mosaic in the bathhouse at Lower Herodium built by Herod the Great, unearthed and visible at the National Museum of Israel. Israel, 20 BC. (Photo credit: © Shmuel Browns, used with permission)
0 – 2000 AD
Broken floor mosaic [item 21]
Broken floor mosaic of pomegranates, fig leaves & geometrical pattern of circles on the reception room in the Western Palace built by Herod the Great. Masada, Israel, 30BC – 70AC. (Photo credit: James Emery)
Roman temple stele [item 22]
A stele from the Roman temple ruins. Córdoba, Spain, 100 – 500 AC. (Photo credit: Steve Pope)
Floor mosaic in Besancon [item 23 a]
Geometrical motifs in the mosaics visible in the Museum of Fine Arts and Archaeology. Besancon, France, Gallo-Roman Period 123 BC – 486 AD. (© Pierre Dupont, Inrap)
Floor mosaic [item 23 b]
Geometrical motifs in the mosaics visible in the Museum of Fine Arts and Archaeology. Besancon, France, Gallo-Roman Period 123 BC – 486 AD. (Photo credit: heroesbed)
Basilica floor mosaic [item 24]
A mosaic floor from the basilica in the town near to Yambol. Kabile, Bulgaria, 400 AD. (Photo source: http://bulstack.com/)
Sassanian bowl [item 25]
A Sassanian inscribed parcel-gilt silver bowl. 400 – 500 AD.
Wall in Syria [item 26]
About 100 kilometers west of Deir az-Zor on the Euphrates river in the Syrian desert is the Ummayad hunting château where wall paintingsresembles much like the drawings of the Leonardo da Vinci. Qasr al-Hair ash-Sharqi, 729 AD.
Pavement [item 27]
A multicolor opaque glass “Cosmati” pavement in the Westminster Abbey Gothic church. London, England, 1268 AD. (Copyright: Dean and Chapter of Westminster)
Hampi pillar [item 28]
The Flower of Life symbol in the pillar in the Hampi temple. India, 1400 AD. (Photo credit: Wm Jas)
Cemetery decorations [item 29 a]
Ottoman cemetery headstone decorations from the antique field of ancient Smyrna. Izmir, Turkey, 1400 AD. (Photo credit: Marko Manninen)
Sarcophagus [item 29 b]
An Ottoman sarcophagus in the antique field of ancient Smyrna. Izmir, Turkey, 1400 AD. (Photo credit: Marko Manninen)
Leonardo da Vinci’s notes [item 30]
Leonardo Da Vinci’s explorations of the hexagonal geometry on hisCodex Atlanticus notebooks, 307 verso. Italy, 1500 AD. (Photo credit: Public Domain)
Six-petal flower lunette [item 31]
A six-petal flower lunette above the door of the Orthodox chapel (upper picture). More complex pattern of the intersecting circles can be seen on both sides of the center circle when picture is zoomed in (lower picture). Patmos, Chora, Greece. Undated. (Photo credit: Marko Manninen)
Jewish painting [item 32]
A Jewish painting that has a Hebrew inscription around the circle of the Flower of Life. Undated.
Assyrian wall decoration [item 33]
Presumably Assyrian wall decoration in the Pergamon Museum in Berlin. Undated. (Photo credit: Sanjin Đumišić)
Fu Dog Sphere [item 34]
An earth sphere under the Fu dog (or male lion/Buddha). This is a common defender statue on the houses and temples in the Ming and Qing dynasties. In the picture is one of the stone lions guarding the Jing’An Temple in Shanghai, China. Undated. (Photo credit: Tyson Amick)
Sikh temple marble floor [item 35]
A Sikh temple marble floor decoration. Amritsar, India. Undated.
Mosaic floor in Pompeii [item 36]
Mosaic floor in the House of Tragic Poet as House of Glaucus. Italy, Pompeii. Undated.
Mosaic floor in Seville [item 37]
Mosaic in the Archeological Museum of Seville, Spain. Undated. (Photo credit: Rafael del Pino)
Map of flowers
The map below shows the places where the collected artifacts were found as well as their assumed dating:
I think it is far too early to do any firm specific conclusions of the FOL symbol. Dating of the symbol is hard as it is usual when trying to trace ancient inventions. Often we can talk only in accuracy of thousands years, rather than hundreds. But it is clear that history of the FOL goes further than many expects. It makes sense that six-petal rosette came first preceding rhombus, triangle and zig-zag patterns which themselves goes to the neolithic periods and beyond. But how long it took to develop from six rayed rosettes to the continuous flower pattern? We do need classifications to group different types of the pattern, to distinguish the development of the symbol from simple parts to the complex form.
Other interesting questions are the development of the drafting compass (or its simple fixed variation called divider or caliper), accuracy and skills of using tools that were required to construct the pattern. Quite often it is believed that Egyptians didn’t possess the compass, that they were mere rope stretchers (common example: L.R. Shelby: Medieval Masons’ Tools, page 237). In contrast to this we can see oldest objects in the current survey coming from Egypt indeed! Anyone can make own conclusions if those lid carvings [item 2] were made with a help of a rope or more accurate fixed or adjustable compass with sharp and durable endpoints. Museum object descriptions are pro to a compass. However following this line to get more information about the FOL is kind of a dead end because history of the compass in behalf of artifacts can be traced to the around 600 BC only. Are we thus forced to follow a more intuitive path and face the old Greek myth of Perdix, who was assumed to invent a pair of compasses and a saw? Legend tells that a zig-zag figured saw was made from the spine of a fish.
As it is with dating, it is with locating. Where did sophisticated sense of the geometric forms develop to such a degree that the FOL was in ability of human mind ready to be created? We shouldn’t forget that for example design of the Samarra period dishes are truly amazing while they go as far as 7500 years back to the history. See these plates for example (© Journal of Near Eastern Studies):
What was the meaning of the FOL then? It is unlikely that the name and the meaning was carried out from millenium to millenium and through different cultures unchanged and same. Sometimes symbol was probably used as an interesting decoration and ornament, pleasing and exciting on the eye of an artisan, maybe without any specific name. Sometimes it appears clearly on a religious context. Later, when I’m struggling more with the mathematical and geometrical properties of the FOL, I will present possible meanings and names attached to the symbol.
- Drunvalo Melchizedek: The ancient secret of the Flower of Life, Vol. 1&2 (1999 & 2000)
- Eleanor Robson: Mesopotamian mathematics (1999)
- Eleanor Robson: The apsamikku in Neo-Babylonian Mathematics (2007)
- Joran Friberg: A remarkable collection of Babylonian mathematical texts (2007)
- Duncan J. Melville: Some old Babylonian geometry (2005)
- B.J. McCartin: Mysteries of the equilateral triangle (2010)
- B.B. Shefton: Greek vases (1989)
- Pauline Albenda: Assyrian carpets in stone (1978)
- Stephen Wolfram: A new kind of science (2002)
- Serçe Limani: An Eleventh-Century Shipwreck Vol. 1, The Ship and Its Anchorage, Crew, and Passenger (2004)
- E.R. Goodenough: Jewish Symbols in the Greco Roman, Vol. 5 & 7 (1958)
- D.T. Potts: A Companion to the Archaeology of the Ancient Near East (2012)
- Georgina Herrmann, Stuart Laidlaw: Ivories from Nimrud VI (2008)
- Beatrice Teissier: Ancient Near Eastern Cylinder Seals from the Marcopoli Collection (1984)
This list of the keywords and combinations of them can be used to search more information about the FOL and related topics on libraries and search engines:
flower of life, six-petal rosette, six rayed star, six spoked wheel, rosette, apsamikku(m), conclave square, square root of 3, intersecting circles, hexagon, equilateral triangle, rhombus, vesica piscis, goblet, beaker, pyxis, cosmetic lid, ivory, mosaic, cylinder seal, sacred geometry.