## Conway symmetry for polygonsPolytile notation only concerns itself with cyclic/rotational symmetry. We may also be interested in reflectional symmetry. John H. Conway presented a system that applies to all planar polygons. It uses a letter class followed by the symmetry order. Conway defines 5 symmetry classes: -
**a**=asymmetric (no symmetry), -
**g**=gyrosymmetric (rotational symmetry only), -
**r**=regular (reflections on vertices and edges), -
**p**=persymmetric (reflections passing through edges), -
**d**=diasymmetric (reflections pass through vertices), and -
**i**=isosymmetry (reflections pass through both vertices and edges).
Reflectional symmetry orders are doubled from a gyration symmetry. We may
add these names to qualify a given polytile:
We can inspect polytile notation to determine the symmetry. A
A p-tile with reflectional symmetry will have the form:
© 2020 Created by Tom Ruen |