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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?

Answer :

taskmasters
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.
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we know that

The orthorhombic crystal system is one of the seven crystalline systems existing in crystallography. Many minerals crystallize in this type of network, such as olivine or topaz. Orthorhombic crystal system is also known as the rhombic system.In this system there are three axes, all of which meet at 90 degrees to each other. However, all the axes are a different length

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therefore

the answer is

The orthorhombic crystal system

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