The unit cell of topaz is made of three pairs of rectangular faces, each pair a different size than the others. the faces are oriented at 90 degree angles to one another. what type of crystal system is this?

The type of crystal system that has been described in the question is called orthorhombic crystal system. In case of this system, the latices result from the stretching of the cubic lattice along two of its orthogonal pairs by two different factors. I hope that this is the answer that has come to your desired help.

X^2 - 4x +(4/2^2) + y^2 + 8y + (8/2^2) = -4 + (4/2^2) + (8/2^2)(x + 2)^2 + (y + 4)^2 = -4 + 4 + 16your center is (-2, -4) and the radius is the sqrt of -4 + 4 + 16 which is 4