HOME | DD

Description
Flash MX 2004, 4 hours.

vvvv Another way of viewing can be found here vvvv

[link]

These shapes are based upon the principle of dividing the circle (henagon) into equal arcs by the number in the left hand column of the chart. [link]

Take note that the suffix 'gon' refers to a polygon, a shaped formed by a perimeter of straight lines. The suffix 'gram' simply means 'line' which in this case is the star form of the radially symmetric, segmented polygon.

Here are their names (wikipedia links among them)

3 - Triangle/Trigon [link]
4 - Square/Tetragon [link]
5 - Pentagon [link] , Pentagram [link] [link]
6 - Hexagon [link] , Hexagram [link]
7 - Septegon/Heptagon [link] , Septegram/Heptagram [link]
8 - Octogon, Octogram [link]
9 - Nonagon/Enneagon [link] , Nonagram/Enneagram [link]
10 - Decagon [link] , Decagram geometry
11 - Hendecagon [link] , Hendecagram [link]
12 - Dodecagon [link] , Dodecagram [link]
13 - Triskaidecagon/Tridecagon [link] , Triskaidecagram/Tridecagram

All of the shapes in the first column are the divided circles, with lines connecting every point possible within that circle, minus diameter lines (lines that travel through the center of the circle). Many shapes are born in this process- starting with the least complex 2D shape next to the circle, a triangle. You'll notice that every odd number and its following even number have an equal amount amount of unique shapes that are possible, and that increases with every 2 steps (starting on an odd number)

For my art, I enjoy drawing 3 dimensional (and impossible) interlacing interpretations of these figures. Like these:

[link]
[link]
[link]

There are two types of interlacing, continuous and no-continuous.

The very first shape with the ability to interlace is the Pentagram, (which simply means "five lines" everybody, not "I love Satan") on row 5, column 2. It interlaces continuously, meaning you can follow a line and it connects to itself like a complex infinity loop. Other shapes that interlace continuously are:

Septegrams, all variants, 7 is a prime number
Octagram (row 8, column 2)
Nonagrams, (row 9, columns 2,4)
Decagrams, (row 10, columns 2,3)
Hendecagrams, all variants, 11 is a prime number
Dodecagrams, (row 12, column 2)
Triskaidecagram, all variants, 13 is a prime number

The first shape to interlace non-continuously is the Six Pointed (David's) Star, also known as the Hexagram. Like the Pentagram, this shape skips one of its points to form a star shape, but being an even number, it cannot connect with itself with the same "skip one" concept. The Hexagram is simply made of two triangles, but never share the path of a line. The same is true for the "skip one" variants of every even numbered figure acts the same way- the Octagram on row 8, column 3 is made of two squares. Also, any figure with a number divisible by a number equal to or greater than three also has the ability to interlace non-continuously. The first is of course the Hexagram, (6 divided by a triangle- 3, equals 2 triangles). The first one to interlace non-continuously with more than 2 shapes is the Nonagram on row 9, column 3 (9 divided by a triangle- 3, equals 3 triangles). It is not possible for any figure with a prime number of points to interlace non-continuously, since they cannot divide by any whole number.

One more very interesting thing to note is that; without any exception, the column 2 shapes contain every lesser consecutive shape within themselves. The Pentagram contains a Pentagon in it's center, the Septagram contains the lesser Septagram variant, which in turn contains a Septagon. This same pattern works for every shape on this chart and into infinity.

(Edited 2010-08-28)

Description
Flash MX 2004, 4 hours.

vvvv Another way of viewing can be found here vvvv

[link]

These shapes are based upon the principle of dividing the circle (henagon) into equal arcs by the number in the left hand column of the chart. [link]

Take note that the suffix 'gon' refers to a polygon, a shaped formed by a perimeter of straight lines. The suffix 'gram' simply means 'line' which in this case is the star form of the radially symmetric, segmented polygon.

Here are their names (wikipedia links among them)

3 - Triangle/Trigon [link]
4 - Square/Tetragon [link]
5 - Pentagon [link] , Pentagram [link] [link]
6 - Hexagon [link] , Hexagram [link]
7 - Septegon/Heptagon [link] , Septegram/Heptagram [link]
8 - Octogon, Octogram [link]
9 - Nonagon/Enneagon [link] , Nonagram/Enneagram [link]
10 - Decagon [link] , Decagram geometry
11 - Hendecagon [link] , Hendecagram [link]
12 - Dodecagon [link] , Dodecagram [link]
13 - Triskaidecagon/Tridecagon [link] , Triskaidecagram/Tridecagram

All of the shapes in the first column are the divided circles, with lines connecting every point possible within that circle, minus diameter lines (lines that travel through the center of the circle). Many shapes are born in this process- starting with the least complex 2D shape next to the circle, a triangle. You'll notice that every odd number and its following even number have an equal amount amount of unique shapes that are possible, and that increases with every 2 steps (starting on an odd number)

For my art, I enjoy drawing 3 dimensional (and impossible) interlacing interpretations of these figures. Like these:

[link]
[link]
[link]

There are two types of interlacing, continuous and no-continuous.

The very first shape with the ability to interlace is the Pentagram, (which simply means "five lines" everybody, not "I love Satan") on row 5, column 2. It interlaces continuously, meaning you can follow a line and it connects to itself like a complex infinity loop. Other shapes that interlace continuously are:

Septegrams, all variants, 7 is a prime number
Octagram (row 8, column 2)
Nonagrams, (row 9, columns 2,4)
Decagrams, (row 10, columns 2,3)
Hendecagrams, all variants, 11 is a prime number
Dodecagrams, (row 12, column 2)
Triskaidecagram, all variants, 13 is a prime number

The first shape to interlace non-continuously is the Six Pointed (David's) Star, also known as the Hexagram. Like the Pentagram, this shape skips one of its points to form a star shape, but being an even number, it cannot connect with itself with the same "skip one" concept. The Hexagram is simply made of two triangles, but never share the path of a line. The same is true for the "skip one" variants of every even numbered figure acts the same way- the Octagram on row 8, column 3 is made of two squares. Also, any figure with a number divisible by a number equal to or greater than three also has the ability to interlace non-continuously. The first is of course the Hexagram, (6 divided by a triangle- 3, equals 2 triangles). The first one to interlace non-continuously with more than 2 shapes is the Nonagram on row 9, column 3 (9 divided by a triangle- 3, equals 3 triangles). It is not possible for any figure with a prime number of points to interlace non-continuously, since they cannot divide by any whole number.

One more very interesting thing to note is that; without any exception, the column 2 shapes contain every lesser consecutive shape within themselves. The Pentagram contains a Pentagon in it's center, the Septagram contains the lesser Septagram variant, which in turn contains a Septagon. This same pattern works for every shape on this chart and into infinity.

(Edited 2010-08-28)