icosahedral virus (with 5 3 2 symmetry)
Game Introduction
I drew this in photoshop, built the 3D model with paper, then with Blender software to make what's shown here. The icosahedron joins up triangles all with the same rules of connection, just repeated over and over. The simplicity of the rules means that we can build the structures with minimal instruction. For this reason, nature builds many virus shells in the icosahedral or dodecahedral shapes. To build these virus shells requires minimal rules, which means minimal genetic code (DNA). Although an icosahedral virus shell has lots of symmetry, it lacks mirror symmetry because the proteins that make up each triangle unit of the shell turn in one direction. Each of the triangles in this virus icosahedron is made of three proteins. The trio of proteins creates a shape that turns in one direction, so there is no mirror symmetry. That twist in the proteins breaks the mirror symmetry. But like any regular icosahedron, each corner joins five triangles, so there is a five-fold rotational symmetry. You can rotate the virus around a corner one fifth of a turn and end up with the same pattern. You can play around with a model of an icosahedral virus to see the other symmetries. You can rotate the virus around the center of a triangle a third of a turn or two thirds of a turn, and you will see the same pattern as before. Also, you can rotate the shape at the point in the middle of the side of any triangle and end up with the same pattern. So, there is a five-fold, three-fold, and a two-fold symmetry in this icosahedron, called a 5 3 2 symmetry. That's the way a crystallographer would describe it.
How To Play
Many viruses are icosahedral. Each triangle in this particular virus icosahedron is made of three proteins which creates a shape that turns in one direction. So there is no mirror symmetry. But like any regular icosahedron, each corner joins five triangles, so there is a five-fold rotational symmetry. There is a five-fold, three-fold, and a two-fold symmetry in this icosahedron, called a 5 3 2 symmetry.
Author
crkcity
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Game Information
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