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We examine the recently found point of intersection between the Z_2 and Z_4 orbifold subvarieties in the K3 moduli space more closely. First we give an explicit identification of the coordinates of the respective Z_2 and Z_4 orbifold theories at this point. Secondly we construct the explicit identification of conformal field theories at this point and show the orthogonality of the two subvarieties.doi:10.1088/1126-6708/2004/08/015 fatcat:arb6g2gdljdvjm6h4dwdrrkmji