Each unit cell is characterized by three basis vectors, **a**_{1}, **a**_{2}, and **a**_{3}, which lie along the *x*, *y*, and *z* coordinate axes. The Kelvin unit cell consists of six identical square frames forming a cubic lattice with direct lattice vectors $a1=(22L,0,0),a2=(0,22L,0)$, and $a3=(0,0,22L)$ The direct lattice vectors for the octet lattice are $a1=(2L,0,0),a2=(0,2L,0)$, and $a3=(0,0,2L)$ and those of both simple- and framed-cubic lattice are $a1=(L,0,0),a2=(0,L,0)$, and $a3=(0,0,L)$, where *L* is the strut length. The infinite periodic material is described by a primitive unit cell, $U$ and spatially traversed through lattice vectors **a**_{1}, **a**_{2}, and **a**_{3} so that the position of any point *p* within an arbitrary cell of the infinite periodic lattice can be expressed by
Display Formula

(1)$rp=r0+n1a1+n2a2+n3a3$