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Hizashi Subfamily
Article © MAIL User: Drax
The Hizashi Subfamily of Japanese Weaves
by Drax
This article draws a lot of information from another that I wrote on tessellations and the theory of Japanese weaves. Check out that article here (I’ll make link after this is copied from the test site) for background on tessellations and how they work with these weaves.
I created (or discovered, if you will) the hizashi subfamily using the tessellation theory. The name 'hizashi' is Japanese for sunrays. I think the reason for this name will become clear with the information here. This subfamily actually contains an endless number of members.
The first member of the hizashi subfamily is shown below, along with the tessellation pattern that I used to make it (the grid shows a larger portion of the weave than the physical example).
The blue lines represent the only sections of the weave that are 6in1. It is 5in1 everywhere else. (Notice one could remove this 6in1 link, then the entire piece becomes 4in1). This is a general characteristic of the Hizashi family.
I chose the name hizashi because I look at the hexagons (the triangle clusters) as suns, and the squares that connect them as rays. This becomes more obvious by looking at the third member of the hizashi subfamily as shown below, Hizashi3:
I number hizashi by counting the number of squares that run in between each hexagon section.
Now, at this point I haven't made Hizashi2 with rings, but I know it will look like this:
The number of Hizashi possible is endless. One could construct Hizashi1-HizashiN (where N=infinity), not to mention variations even within this family; for instance one can leave out the central ring of the hexagonal clusters of triangles. This will create a more net-like weave, as shown in these brief renditions of the first three Hizashi:
Of course, with the tessellation theory of Japanese weaves in place, and with the endless variation of tessellations (and thus weaves) possible, it may not be such a good idea to keep naming all of them. A nomenclature system for tessellations does exist, and it is not so difficult to understand. You can find more information on it at http://library.thinkquest.org/16661/index2.html.
Basically this numbering scheme identifies the polygons located around a vertex (where the shapes meet); you identify the polygons with a number equal to the number of sides of the shape (triangles = 3, square = 4, etc). To start, you find a shape with the fewest number of sides in the pattern and travel around the vertex numbering all the polygons (if there's a run of smallest shapes, travel in that direction first). So Hizashi1 turns out to be 3.4.6.4.
In most cases, the verticies will all be the same (for regular tessellations), but for semi- and demi-regular tessellations, you will probably need to name more than one vertex. An example of this is Hizashi3, which is 3.3.3.3.3.3/3.3.3.4.4/3.3.4.3.4. Whew! For a more thorough and clear definition of this nomenclature system, see the aforementioned website.
by Drax
This article draws a lot of information from another that I wrote on tessellations and the theory of Japanese weaves. Check out that article here (I’ll make link after this is copied from the test site) for background on tessellations and how they work with these weaves.
I created (or discovered, if you will) the hizashi subfamily using the tessellation theory. The name 'hizashi' is Japanese for sunrays. I think the reason for this name will become clear with the information here. This subfamily actually contains an endless number of members.
The first member of the hizashi subfamily is shown below, along with the tessellation pattern that I used to make it (the grid shows a larger portion of the weave than the physical example).
The blue lines represent the only sections of the weave that are 6in1. It is 5in1 everywhere else. (Notice one could remove this 6in1 link, then the entire piece becomes 4in1). This is a general characteristic of the Hizashi family.
I chose the name hizashi because I look at the hexagons (the triangle clusters) as suns, and the squares that connect them as rays. This becomes more obvious by looking at the third member of the hizashi subfamily as shown below, Hizashi3:
I number hizashi by counting the number of squares that run in between each hexagon section.
Now, at this point I haven't made Hizashi2 with rings, but I know it will look like this:
The number of Hizashi possible is endless. One could construct Hizashi1-HizashiN (where N=infinity), not to mention variations even within this family; for instance one can leave out the central ring of the hexagonal clusters of triangles. This will create a more net-like weave, as shown in these brief renditions of the first three Hizashi:
Of course, with the tessellation theory of Japanese weaves in place, and with the endless variation of tessellations (and thus weaves) possible, it may not be such a good idea to keep naming all of them. A nomenclature system for tessellations does exist, and it is not so difficult to understand. You can find more information on it at http://library.thinkquest.org/16661/index2.html.
Basically this numbering scheme identifies the polygons located around a vertex (where the shapes meet); you identify the polygons with a number equal to the number of sides of the shape (triangles = 3, square = 4, etc). To start, you find a shape with the fewest number of sides in the pattern and travel around the vertex numbering all the polygons (if there's a run of smallest shapes, travel in that direction first). So Hizashi1 turns out to be 3.4.6.4.
In most cases, the verticies will all be the same (for regular tessellations), but for semi- and demi-regular tessellations, you will probably need to name more than one vertex. An example of this is Hizashi3, which is 3.3.3.3.3.3/3.3.3.4.4/3.3.4.3.4. Whew! For a more thorough and clear definition of this nomenclature system, see the aforementioned website.
Original URL: http://www.mailleartisans.org/articles/articledisplay.php?key=4
