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?

The correct answer is Auguste Bravais.

 Key Points

•  Auguste Bravais was a French physicist who demonstrated in 1848 that there are only 14 possible three-dimensional lattices that can fill space without gaps, known as Bravais lattices.
• Bravais Lattice refers to the 14 different 3-dimensional configurations into which atoms can be arranged in crystals.
• The smallest group of symmetrically aligned atoms which can be repeated in an array to make up the entire crystal is called a unit cell.
• In words, a Bravais lattice is an array of discrete points with an arrangement and orientation that look exactly the same as any of the discrete points, that is the lattice points are indistinguishable from one another.

 Additional Information

• William Bragg (1862-1941) was a British physicist known for his work on X-ray crystallography, developed alongside his son Lawrence Bragg.
• Jerome Karle (1918-2013) and Charles Frank (1911-1995) were American crystallographers who made significant contributions to the field in the 20th century.