Enneagram (geometry)
Encyclopedia
In geometry
, an enneagram is a nine-pointed geometric figure. It is sometimes called a nonagram.
but connected in fixed steps. It has two forms, represented by a Schläfli symbol as {9/2} and {9/4}, connecting every second and every fourth points respectively.
There is also a star figure, {9/3} or 3{3}, made from the regular enneagon points but connected as a compound of three equilateral triangles. (If the triangles are alternately interlaced, this results in a Brunnian link
.) This star figure is sometimes known as the star of Goliath, after {6/2} or 2{3}, the star of David
.
This geometrical figure should not be confused with the logic puzzles called nonograms.
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, an enneagram is a nine-pointed geometric figure. It is sometimes called a nonagram.
Regular enneagram
A regular enneagram (a nine-sided star polygon) is constructed using the same points as the regular enneagonEnneagon
In geometry, a nonagon is a nine-sided polygon.The name "nonagon" is a prefix hybrid formation, from Latin , used equivalently, attested already in the 16th century in French nonogone and in English from the 17th century...
but connected in fixed steps. It has two forms, represented by a Schläfli symbol as {9/2} and {9/4}, connecting every second and every fourth points respectively.
There is also a star figure, {9/3} or 3{3}, made from the regular enneagon points but connected as a compound of three equilateral triangles. (If the triangles are alternately interlaced, this results in a Brunnian link
Brunnian link
In knot theory, a branch of mathematics, a Brunnian link is a nontrivial link that becomes trivial if any component is removed. In other words, cutting any loop frees all the other loops ....
.) This star figure is sometimes known as the star of Goliath, after {6/2} or 2{3}, the star of David
David
David was the second king of the united Kingdom of Israel according to the Hebrew Bible and, according to the Gospels of Matthew and Luke, an ancestor of Jesus Christ through both Saint Joseph and Mary...
.
This geometrical figure should not be confused with the logic puzzles called nonograms.
Complete graph Complete graph In the mathematical field of graph theory, a complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique edge.-Properties:... K9 |
 Enneagon Enneagon In geometry, a nonagon is a nine-sided polygon.The name "nonagon" is a prefix hybrid formation, from Latin , used equivalently, attested already in the 16th century in French nonogone and in English from the 17th century... {9/1} |
 Star polygon {9/2} |
 Star figure 3{3} |
 Star polygon {9/4} |
Other enneagram figures
 The final stellation of the icosahedron Final stellation of the icosahedron In geometry, the complete or final stellation of the icosahedron is the outermost stellation of the icosahedron, and is "complete" and "final" because it includes all of the cells in the icosahedron's stellation diagram.... has 2-isogonal enneagram faces. It is a 9/4 wound star polyhedron, but the vertices are not equally spaced. |
 The Enneagram of Personality Enneagram of Personality The Enneagram of Personality is a model of human personality which is principally used as a typology. Principally developed by Oscar Ichazo and Claudio Naranjo, it is also partly based on earlier teachings of G. I. Gurdjieff... and the Fourth Way Fourth Way Enneagram The Fourth Way enneagram is a figure published in 1947 in In Search of the Miraculous by P.D. Ouspensky, and an integral part of the so-called Fourth Way esoteric system associated with George Gurdjieff... teachings use an irregular enneagram consisting of a triangle and an irregular hexagram. |
 The Bahá'í nine-pointed star |
Use in popular culture
- SlipknotSlipknot (band)Slipknot is an American heavy metal band from Des Moines, Iowa. Formed in 1995, the group was founded by percussionist Shawn Crahan and bassist Paul Gray...
, a heavy metalHeavy metal musicHeavy metal is a genre of rock music that developed in the late 1960s and early 1970s, largely in the Midlands of the United Kingdom and the United States...
band, uses the |9/3| star figure enneagram as a symbol. - The nine-pointed star or enneagram can symbolize the nine gifts or fruits of the Holy Spirit.
See also
- Nonagon (enneagon)
- List of regular star polygons