Consider the reduced-sphere unit cell shown in Problem 3.23, having an origin of the coord...

Consider the reduced-sphere unit cell shown in Problem 3.23, having an origin of the coordinate system positioned at the atom labeled O. For the following sets of planes, determine which are equivalent:

(a) (100), (010), and (001)

(b) (110), (101), (011), and (101)

(c) (111), (111), (111), and (111)

Problem 3.23

The accompanying figure shows a unit cell for a hypothetical metal.

(a) To which crystal system does this unit cell belong?

---

(b) What would this crystal structure be called?

---

(c) Calculate the density of the material, given that its atomic weight is 141 g/mol.