The Brillouin zone is a concept in solid-state physics and crystallography. It is a mathematical representation of the allowed states of an electron in a crystalline solid within the framework of quantum mechanics. The Brillouin zone is used to describe the behavior of electrons in a crystal lattice and plays a crucial role in understanding the electronic properties of materials. For a body-centered cubic (BCC) unit cell, the Brillouin zone is a polyhedron in reciprocal space. The specific shape and size of the Brillouin zone depend on the crystal lattice structure. In the case of BCC, the Brillouin zone is often a truncated cube.
In this simulator, for three face-centered cubic lattices, it displays the perpendicular bisecting planes in reciprocal space. Through the visualization of six perpendicular bisecting planes, you can confirm the actual creation of a rhombus, which is one face of the dodecahedron.
please access to below link:
https://ryoaki374.github.io/Burillounian-zone/
This simulator is rendered using three.js and HTML5 canvas.