Finite Fields
When working over finite fields, one defines a "reflection" as a map that fixes a hyperplane (otherwise for example there would be no reflections in characteristic 2, as so reflections are the identity). Geometrically, this amounts to including shears in a hyperplane. Reflection groups over finite fields of characteristic not 2 were classified in (Zalesskiĭ & Serežkin 1981).
Read more about this topic: Reflection Group
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“For it is only the finite that has wrought and suffered; the infinite lies stretched in smiling repose.”
—Ralph Waldo Emerson (1803–1882)
“The landscape was clothed in a mild and quiet light, in which the woods and fences checkered and partitioned it with new regularity, and rough and uneven fields stretched away with lawn-like smoothness to the horizon, and the clouds, finely distinct and picturesque, seemed a fit drapery to hang over fairyland. The world seemed decked for some holiday or prouder pageantry ... like a green lane into a country maze, at the season when fruit-trees are in blossom.”
—Henry David Thoreau (1817–1862)