[alogo] Composition of three reflexions

ABC the basic triangle. l, m, n the reflexions on its sides BC, CA, AB respectively. Their composition f= m*l*n is a "Glide-Reflexion", with axis the side FE of the orthic triangle DEF and translation-vector GH equal to the perimeter of the orthic triangle.
The cyclic permutations l*n*m and n*m*l give glide-reflexions with respect to the other sides of the orthic triangle. The remaining permutations give inverse transformations to those three.

[0_0] [0_1] [0_2] [0_3]
[1_0] [1_1] [1_2] [1_3]

Glide-reflexions are compositions of reflections on an axis "e" and translation by a vector "v", parallel to "e".

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