Symmetry Group P31M can easily be confused with P3M1 which has 3 different mirror reflections. I’ve made the mistake often (more on this in previous post). This group has a three-fold rotation point in the middle of an equilateral triangle. Three identical mirrors surrounding the shape.
If one single line is drawn, from one of the 3 points, to the center of the triangle, you will create a single, repeating shape. With a bit of tweaking, the single green line below could be turned into frogs or geckos.
The Manta Rays below show one simple line from a triangle’s peak point, to the center, creates the shape. A secondary minor line complete the mouth. A fun rule to play with.
Omega Boy, one my first drawings completed with KaleidoPaint. The basic line follows the top of the head, along the mirror plane, then curves down to the neck, shoulder and arm to the middle rotation point. A secondary minor line completes his cape.
Lots of software out there to help you accomplish this type of design.
An iPad app is available, which is what I have used here to create these images: KaleidoPaint by Jeff Weeks.
There is also a java-based program “Escher Web Sketch” at the Ecole Polytechnique de Lausanne. Make sure Java is enabled and not blocked by your security software.
Also, another screen-based software by Anselm Levskaya Escher Sketch v2. (I used to have a basic Mac-based software, way back in prehistory, 1995, by the same name. It worked on the cutesy first Mac)
Or a pair of scissors and a piece of cardboard works quite well. That’s how I learned.
Comments are always welcome!