Now we look for the envelope of the set of WALLACE-lines of a triangle ABC. With CINDERELLA we can create this envelope using the locus mode by selecting the point X as the mover, the circumcircle u as the road and the WALLACE-line of X as the tracer. The result is the hypocycloid of STEINER with three cuspidal points and the circumcentre N of the NINE-POINT circle as the centre of a three axes symmetry. There is an interesting relationship with the MORLEY-triangle of the triangle ABC too.

Figure 3 shows this hypocycloid as the envelope of the set of WALLACE-lines using the animation mode. Figure 4 shows an alternative creation of this hypocycloid as a roulette.