Rough Notes:

Octagram

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Sun of Vergina – A Greek symbol

IN ANCIENT MACEDONIAN ETHNICITY, ARCHAEOLOGY, FYROM PROPAGANDA, MACEDONIAN CULTURE, MACEDONIAN SYMBOLS, SKOPJAN PROPAGANDA / BY  / ON APRIL 10, 2008 AT 1:24 PM /

Το Αστέρι της Βεργίνας – Ένα Πανελλήνιο Σύμβολο

 

The Sun of Vergina is a symbol that was widely used by Ancient Greeks. It became famous due to the Macedonians who were using it as Symbol of the Argead Dynasty.

–The Royal house of Macedon:

vergina sun philip

The typical Sun of Vergina is a 16-pointed Sun. It can also be found in other styles: 12-pointed or 8-pointed. What was the meaning of this symbol?? –In the typical 16-pointed Sun , the 4 rays represent the 4 elements: Earth-Ocean-Fire-Air. The other 12 rays represent the 12 Gods of Olympus.You can see the explanation in the following animation :

–In every form, the Sun of Vergina symbolized Virginity:

Goddess Athena was a Virgin, so this Sun was associated with her. We can also find this symbol associated with Apollo. –All the versions (16,12 and 8-pointed Sun) are associated with another famous Greek symbol, the “Delphian Epsilon”, symbol of Apollo: 

 

The Sun of Vergina became common art design in coins, craters, wall-drawings etc LONG BEFORE the Macedonian royal house (the Argead Dynasty) used it. After the unification of the Greek (Hellenic) nation under the leadership of Alexander the Great, the Sun of Vergina became the symbol of the Hellenic Ethnogenesis.

In the following replies, you will be able to see some pieces of Ancient Greek art containing the Sun of Vergina, BEFORE THE RISE OF THE GREEK KINGDOM OF MACEDONIA. These sun symbols are found in various Greek places, apart from Macedonia. Moreover, there will be a small historical flashback, in order to see the evolution of this symbol throught the ages :

2000 BC:

This is the time where ancient Greeks first started using the Sun symbol. It was not standardized yet, it was a early form of the Sun of Vergina:

780BC:

The Sun of Vergina has been standardized. The following art work shows the destruction of Troy. We can clearly see the Sun symbol in the warrior’s hump. It was found in Mykonos island :

The following images are just a small sample, showing the wide usage of the Sun of Vergina in Greek Art:

Spartan Hoplite – 780 BC:

Spartan Amphoreus –

It dates from the 6th century BC, that is, well before Macedonia’s later dominance in the Greek world. In this fine example of ancient pottery, the Sunburst here is not just an incidental decorative motif but rather constitutes the central theme. Its appearance on this household item from distant Sparta, at such an early date, is one of the most compelling pieces of evidence for the panhellenic nature of this ancient symbol. In addition, this item perhaps alludes to a more specific connection between Sparta and her Dorian cousin of the north.
 

This vase can now be found in the Louvre Museum, Paris. 6th Century BC:

 
An amphora from the Pontus region (the southern shore of the Black Sea) dating from the second half of the sixth century BC. Priam and the god Hermes lead Hera, Athena and Aphrodite to Paris whose task will be to decide which of these goddesses is the most beautiful. According to the legend each of these goddesses made offers to Paris so that they might win the contest. Hera promised to make him ruler of the world, Athena vowed that he would never be vanquished in battle. Paris eventually chose Aphrodite as she promised him the love of Helen, the most beautiful mortal woman in the world. The Trojan War was a direct result of this fateful contest:
 

Exekias was a famous vase-painter and potter of ancient Athens. The scene on this page, from an amphora of the third quarter of the 6th century BC (now at the National Museum of Athens), is one of his most famous works. It is considered one of the finest surviving examples of ‘Black Figure’ vase painting.

Achilles and Ajax, two major Greek heroes of Homer’s Iliad are depicted here relaxing over a game of dice during a lull in the fighting. Achilles has just won; he has just thrown a ‘four’ while Ajax has to accept a ‘three’:

Third Quarter of the 6th century BC:

Achilles and Ajax

The cloaks of both these Homeric figures are studded with numerous 8-ray Sunbursts.

The return of Hephestus– 560 BC:

Below is a pyxis (box-like vase) from the second half of the 6th century BC signed by the prolific Athenian potter Nikosthenes. It depicts the hero Herakles with the Gods of Olympus. The seal on the lid of this vessel features the familiar 16-ray Sunburst. Like the garments of Achilles and Ajax on the Exekias vase, the clothes of one of the figures on the front of the pyxis is also adorned with sunbursts:
 

Athena and Hermes– 540 BC

heracles olympians pyxis     Athena and hermes

Read more http://history-of-macedonia.com/2008/04/10/sun-of-vergina-a-greek-symbol/

 
Regular octagram
Regular star polygon 8-3.svg

A regular octagram
Type Regular star polygon
Edges and vertices 8
Schläfli symbol {8/3}
t{4/3}
Coxeter diagram CDel node 1.pngCDel 8.pngCDel rat.pngCDel d3.pngCDel node.png
CDel node 1.pngCDel 4.pngCDel rat.pngCDel d3.pngCDel node 1.png
Symmetry group Dihedral (D8)
Internal angle(degrees) 45°
Dual polygon self
Properties star, cyclic, equilateral, isogonal, isotoxal

In geometry, an octagram is an eight-angled star polygon.

The name octagram combine a Greek numeral prefix, octa-, with the Greek suffix -gram. The -gram suffix derives from γραμμή (grammḗ) meaning "line".[1]

Detail[edit]

A regular octagram with each side length equal to 1

In general, an octagram is any self-intersecting octagon (8-sided polygon).

The regular octagram is labeled by the Schläfli symbol {8/3}, which means an 8-sided star, connected by every third point.

Variations[edit]

These variations have a lower dihedral, Dih4, symmetry:

Regular truncation 4 1.5.svg
Narrow
Regular truncation 4 2.svg
Wide
(45 degree rotation)		 Isotoxal octagram.png
Octagram-in-square.svg
Isotoxal		 Ancient mapuche flag.svg
An old Flag of Chile contained this octagonal star geometry with edges removed.		 Star Guñelve.svg
The geometry can be adjusted so 3 edges cross at a single point, like the Auseklissymbol		 Compass rose en 08p.svg
An 8-point compass rose can be seen as an octagonal star, with 4 primary points, and 4 secondary points.

The symbol Rub el Hizb is a Unicode glyph ۞  at U+06DE.

As a quasitruncated square[edit]

Deeper truncations of the square can produce isogonal (vertex-transitive) intermediate star polygon forms with equal spaced vertices and two edge lengths. A truncated square is an octagon, t{4}={8}. A quasitruncated square, inverted as {4/3}, is an octagram, t{4/3}={8/3}.[2]

The uniform star polyhedron stellated truncated hexahedron, t'{4,3}=t{4/3,3} has octagram faces constructed from the cube in this way.

Isogonal truncations of square and cube
Regular Quasiregular Isogonal Quasiregular
Regular quadrilateral.svg
{4}		 Regular polygon truncation 4 1.svg
t{4}={8}		 Regular polygon truncation 4 2.svg Regular polygon truncation 4 3.svg
t'{4}=t{4/3}={8/3}
Regular Uniform Isogonal Uniform
Cube truncation 0.00.png
{4,3}		 Cube truncation 0.50.png
t{4,3}		 Cube truncation 3.50.png Cube truncation 2.50.png
t'{4,3}=t{4/3,3}

Star polygon compounds[edit]

There are two regular octagrammic star figures (compounds) of the form {8/k}, the first constructed as two squares {8/2}=2{4}, and second as four degenerate digons, {8/4}=4{2}. There are other isogonal and isotoxal compounds including rectangular and rhombic forms.

Regular Isogonal Isotoxal
Regular star figure 2(4,1).svg
a{8}={8/2}=2{4}		 Regular star figure 4(2,1).svg
{8/4}=4{2}		 Octagram rectangle compound.png Octagram crossed-rectangle compound.png Octagram rhombic star.png

Other presentations of an octagonal star[edit]

An octagonal star can be seen as a concave hexadecagon, with internal intersecting geometry erased. It can also be dissected by radial lines.

2{4} Ashthalakshmi - Star of Laxmi.svg Squared octagonal star.png Squared octagonal star1.png Squared octagonal star2.png
{8/3} Octagram graph.png Octagonal star.png Octagonal star2.png Octagonal star3.png
  Auseklis star.svg Octagonal star-b.png Octagonal star-b2.png Octagonal star-b3.png
  Isotoxal octagram.png Octagonal star-c.png Octagonal star-c2.png Octagonal star-c3.png

Other uses[edit]

  • In Unicode, the "Eight Spoked Asterisk" symbol ✳ is U+2733.

See also[edit]

Usage
Stars generally

References[edit]

  1. Jump up^ γραμμή, Henry George Liddell, Robert Scott, A Greek-English Lexicon, on Perseus
  2. Jump up^ The Lighter Side of Mathematics: Proceedings of the Eugène Strens Memorial Conference on Recreational Mathematics and its History, (1994), Metamorphoses of polygons, Branko Grünbaum
  • Grünbaum, B. and G.C. Shephard; Tilings and Patterns, New York: W. H. Freeman & Co., (1987), ISBN 0-7167-1193-1.
  • Grünbaum, B.; Polyhedra with Hollow Faces, Proc of NATO-ASI Conference on Polytopes ... etc. (Toronto 1993), ed T. Bisztriczky et al., Kluwer Academic (1994) pp. 43–70.
  • John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 26. pp. 404: Regular star-polytopes Dimension 2)

External links[edit]