In the early nineteenth century, who demonstrated that there are fourteen space lattices, or regularly repeating arrangements of points in space, that differ in symmetry and geometry?

Correct option is A

The correct answer is (a) Auguste Bravais.
 Auguste Bravais, a French physicist, demonstrated in the early nineteenth century that there are fourteen distinct space lattices, known as Bravais lattices.
 These lattices represent all possible ways to arrange points in space in a regular and repeating pattern that differ in symmetry and geometry.
 Bravais lattices are fundamental to the study of crystallography and help in understanding the structure of crystals.
Information Booster:
 William Bragg: Known for his work on X-ray crystallography, which led to the determination of crystal structures, along with his son, Lawrence Bragg.
 Jerome Karle: Awarded the Nobel Prize in Chemistry in 1985 for his work on the direct determination of crystal structures using X-ray diffraction.
 Charles Frank: Made significant contributions to the field of crystallography and the understanding of crystal defects, but not specifically related to the demonstration of the fourteen Bravais lattices.