One unit cell for a certain mineral is shown below. The cell has a = 4 , b = 3 , c = 8 , = = 90, and = 100. (a) [5 pts] There are three types of atoms in the cell, illustrated with large, medium, 2 and small spheres. The large atom sits in the body center of the cell, the medium ones are at corners, and the small ones at the midpoints of eight of the 12 edges. How many of each kind of atom are there per unit cell? Show your calculations. (b) [5 pts] For the axis system and origin (0) shown, what are the fractional coordinates of the small atoms labeled P and R? (c) [5 pts] What is the vector from small atom P to small atom R in terms of a, b, and c