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Enneagram | |
---|---|
Enneagrams shown as sequential stellations | |
Edges and vertices | 9 |
Symmetry group | Dihedral (D9) |
Internal angle (degrees) | 100° {9/2} 20° {9/4} |
In geometry, an enneagram is a nine-pointed plane figure. It is sometimes called a nonagram.
The name enneagram combines the numeral prefix, ennea-, with the Greek suffix -gram. The -gram suffix derives from γραμμῆς (grammēs) meaning a line.^{[1]}
A regular enneagram (a nine-sided star polygon) is constructed using the same points as the regular enneagon 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.^{[2]}^{[3]} (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.^{[4]}
Compound | Regular star | Regular compound |
Regular star |
---|---|---|---|
Complete graph K_{9} |
{9/2} |
{9/3} or 3{3} |
{9/4} |
The final stellation of the icosahedron has 2-isogonal enneagram faces. It is a 9/4 wound star polyhedron, but the vertices are not equally spaced. |
The Fourth Way teachings and the Enneagram of Personality use an irregular enneagram consisting of an equilateral triangle and an irregular hexagram based on 142857. |
The Bahá'í nine-pointed star |
The nine-pointed star or enneagram can also symbolize the nine gifts or fruits of the Holy Spirit.^{[5]}
Bibliography