Anandh Subramaniam & Kantesh Balani Parallelepiped is a space filling solid Given a general parallelepiped it is difficult to visualize that it is a space filling shape The following set of slides shows how a parallelepiped can be obtained from a cube- which is easily visualized to be a space filling shape MATERIALS SCIENCE & ENGINEERING Anandh Subramaniam & Kantesh Balani Materials Science and Engineering (MSE) Indian Institute of Technology, Kanpur- 208016 Email: anandh@iitk.ac.in, URL: home.iitk.ac.in/~anandh AN INTRODUCTORY E-BOOK Part of http://home.iitk.ac.in/~anandh/E-book.htm A Learner’s Guide

Start with a simple cubic lattice z y x

Dilate the lattice along the z-direction

Contract the lattice along the z-direction

Shear on the z-plane in the y-direction

A general Parallelepiped