The Geometry of Patches
Posted in Patch Collecting by John E. Pannell on May 11th, 2007 at 12:55 am Geometry, the first and noblest of sciences…
Like many hobbies, collecting patches can be educational.
Order of the Arrow patches preserve part of the history of the Order. They can teach us about past events and officers. The commemorate major events in Scouting. Many depict indigenous animals. With a bit of effort, you can learn about the persons and events that inspired lodges’ names. You might even learn some American history. But did you ever think patch collecting could teach you geometry?
This post will highlight some of the patches shaped like regular polygons.
First I need to give short math lesson for those who are not mathematically inclined. Wikipedia defines a polygon as “…a plane figure that is bounded by a closed path or circuit, composed of a finite number of sequential line segments…” A regular polygon is a polygon with equal angles and sides of the same length. For example a stop sign is a good example of a regular octagon (8 sided regular polygon).
“TRI” is used in Blue Book and this site to denote a triangle. Throughout the years this has been a fairly common shape for patches.
The triangle holds a special significance to Vigil Honor brothers. This meaning is alluded to with the 270 Skyuka L4 pictured to the left.
The Gimogash 214 X1 is arguably the most legendary of triangular shaped patches.
The square is also commonly used as a patch shape, quite often with activities patches . This site and Blue Book denote a square shaped patch with the “SQU” abbreviation.
The 185 X14, issued for the 2004 Dixie Fellowship, is a good example of a square patch.
The standard flap shape is an irregular pentagon. Several patches have been shaped like regular pentagons. Even though it’s not regular, but close, an attractive contemporary pentagonal patch, is the Chilantakoba 397 J2 (pictured).
Classic pentagonal patches also include the X3 and X4 from Jibshe-Wanagan 79. Other irregular pentagons include the Allemakewink 54 P5 and the Quinipissa 479 P2.
Blue Book uses the abbreviation “PEN” to denote a patch with a pentagonal shape.
Another classic shape has been the hexagon. Many of the hexagonal patches are not regular, usually being stretchd vertically. One example of this is the 49 Suanhacky X5. A classic issue that’s almost regular is the eX1957 from Tom Kita Chara 96.
The Golden Sun 492 J1 is an example of a regular hexagon.
I have found only two OA patches take the form of a regular heptagon, namely the 149 X10 and X11 (pictured).
The heptagon is unusual in many ways, one being that it is the lowest order polygon not constructible with a compass and straight edge. Also, its area is only calculable using trigonometry.
The early jacket patches from Blue Heron 349 are among the most beautiful of the “classic” patches. They are very good examples of high quality Swiss style embroidery. They also are good examples of a perfect octagon. Blue Book uses the abbreviation “OCT” to describe this shape.Other patches that are regular octagons include the Ashie 436 J1, C1 and C2 from Kawida 480, the J2 from Gajuka 477, and 2005 activity patches from Talligewi 62.
O-Shot-Caw 265 uses a hendecagon, 11 sided polygon, on its J10a and J10b. Each of the 11 chapter in this lodge have a segment on this patch for themselves, prominently displaying their chapter totem.
I know of no other regular polygons used as patch shapes. Can anyone contradict me and come up with an example of a enneagon (aka “nonagon”, 9 sides), decagon (10 sides), or even a higher order regular polygon?
[...] I had previously written a post titled ”The Geometry of Patches“, highlighting those patches that have taken the shape of regular polygons. In that post I commented that I could not find a lodge or chapter issue that was shaped like a regular decagon. [...]
[...] Last Spring I wrote a post here on “The Geometry of Patches” in which I wrote about various patches shaped like regular polygons.  In that post I lamented about not being able to find a patch shaped as a regular nine-sided polygon (aka enneagon or nonagon).  Well, while working on the price guide earlier this evening I found one! [...]
[...] It’s no secret to those who know me that I have an interest in mathematical things.  I’m one of those crazy folks whose college degree is in mathematics.  In a “prior life” I used to work in the insurance industry. I have even previously written a few posts here on the Geometry of Patches. [...]