[NEEEDS FIX] Discussion:Cartesian Product on 3-Dimensional play of a set $A$ and $B$ for a Hyperrectangle

Cartesian Product of Two Sets for a Hyperrectangle 

By Justin Merchan

Abstract 

Our objective is to create a hyperrectangle by combining two sets of ordered pairs under the concept of a Cartesian product. There will be use triplets in order to apply this practice to a three-dimensional space. 

Introduction

Given two sets $A$ and $B$, where the set of ordered pairs in $A$ are connected by a line, as well as the set of $B$. When $A \times B$, we should get an hyperrectangle (also known as a rectangular prism) Fig. 1a. 

My Solution

Given set $A=\{\alpha,\beta\}$, where $\alpha$ and $\beta$ are represented by the triplets $\alpha=(1,0,0)$ and $\beta=(1,2,0)$; times the set $B=\{a,b,c,d\}$, where $a,b,c,d$ are represented by the triplets, $a=(1,0,0)$; $b=(6,0,0)$; $c=(1,0,-4)$; and $d=(6,0,-4)$. 

Therefore, $A \times B=\{(\alpha,a);(\alpha,b);(\alpha,c);(\alpha,d);(\beta,a);(\beta,b);(\beta,c)(\beta,d)\}$   Fig. 1b.

*Please share with us your answer and final graph if possible. This is an open discussion, so if you catch a mistake, have any question regarding any of the solutions, or you have any opinion in general please comment it.