Math 412. The Orbit Stabilizer Theorem
The orbit of a triangle is the set of all congruent triangles. The stabilizer of an equilateral triangle consists of all the rigid motions which fix the triangle (as a set). This is D 3, basically by definition of D 3. The stabilizer of an isoceles triangle is much smaller: we only have reflections across one axis, so it is a 2-element
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