Geodesic
A Geometrical Construction for the Polynomial Invariants of some Reflection Groups
Serdica Mathematical Journal, Tome 31 (2005) no. 3, pp. 229-242.

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We construct invariant polynomials for the reflection groups [3, 4, 3] and [3, 3, 5] by using some special sets of lines on the quadric P1 × P1 in P3. Then we give a simple proof of the well known fact that the ring of invariants are rationally generated in degree 2,6,8,12 and 2,12,20,30.
Keywords: Polynomial Invariants, Reflection and Coxeter Groups, Group Actions on Varieties 
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Sarti, Alessandra. A Geometrical Construction for the Polynomial Invariants of some Reflection Groups. Serdica Mathematical Journal, Tome 31 (2005) no. 3, pp. 229-242. http://geodesic.mathdoc.fr/item/SMJ2_2005_31_3_a4/