Circumscribed Parallelepiped

This is a drawing of a tetrahedron inscibed in a parallelepiped. See the following reference p. 58-63 S 189 to 202

@BOOK{altshiller1935modern,
title = {Modern pure solid geometry},
publisher = {The Macmillan company},
year = {1935},
author = {Altshiller-Court, N.},
address = {New York},
edition = {first},
lccn = {35024297},
url = {http://books.google.ca/books?id=DDYGAQAAIAAJ}
}

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% Circumscribed Parallelepiped
% Author: Axel Pavillet
\documentclass[tikz,border=10pt]{standalone}
\begin{document}
\begin{tikzpicture}[font=\LARGE] 
% Figure parameters (tta and k needs to have the same sign)
% They can be modified at will
\def \tta{ -10.00000000000000 } % Defines the first angle of perspective
\def \k{    -3.00000000000000 } % Factor for second angle of perspective
\def \l{     6.00000000000000 } % Defines the width  of the parallelepiped
\def \d{     5.00000000000000 } % Defines the depth  of the parallelepiped
\def \h{     7.00000000000000 } % Defines the heigth of the parallelepiped
% The vertices A,B,C,D define the reference plan (vertical)
\coordinate (A) at (0,0); 
\coordinate (B) at ({-\h*sin(\tta)},{\h*cos(\tta)}); 
\coordinate (C) at ({-\h*sin(\tta)-\d*sin(\k*\tta)},
                    {\h*cos(\tta)+\d*cos(\k*\tta)}); 
\coordinate (D) at ({-\d*sin(\k*\tta)},{\d*cos(\k*\tta)}); 
% The vertices Ap,Bp,Cp,Dp define a plane translated from the 
% reference plane by the width of the parallelepiped
\coordinate (Ap) at (\l,0); 
\coordinate (Bp) at ({\l-\h*sin(\tta)},{\h*cos(\tta)}); 
\coordinate (Cp) at ({\l-\h*sin(\tta)-\d*sin(\k*\tta)},
                     {\h*cos(\tta)+\d*cos(\k*\tta)}); 
\coordinate (Dp) at ({\l-\d*sin(\k*\tta)},{\d*cos(\k*\tta)}); 
% Marking the vertices of the tetrahedron (red)
% and of the parallelepiped (black)
\fill[black]  (A) circle [radius=2pt]; 
\fill[red]    (B) circle [radius=2pt]; 
\fill[black]  (C) circle [radius=2pt]; 
\fill[red]    (D) circle [radius=2pt]; 
\fill[red]   (Ap) circle [radius=2pt]; 
\fill[black] (Bp) circle [radius=2pt]; 
\fill[red]   (Cp) circle [radius=2pt]; 
\fill[black] (Dp) circle [radius=2pt]; 
% painting first the three visible faces of the tetrahedron
 
 
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