Icosahedron and Golden Rectangle

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\documentclass{article}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usetikzlibrary{patterns}
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{1pt}
%
% File name: icosahedron-and-golden-rectangle.tex
% Description: 
% A geometric representation of the construction of an icosahedron 
% from three golden rectangles is shown.
% 
% Date of creation: June, 20th, 2021.
% Date of last modification: October, 9th, 2022.
% Author: Efraín Soto Apolinar.
% https://www.aprendematematicas.org.mx/author/efrain-soto-apolinar/instructing-courses/
% Source: page 399 of the 
% Glosario Ilustrado de Matem\'aticas Escolares.
% https://tinyurl.com/5udm2ufy
%
% Terms of use:
% According to TikZ.net
% https://creativecommons.org/licenses/by-nc-sa/4.0/
% Your commitment to the terms of use is greatly appreciated.
%
\begin{document}
%
\begin{center}
\tdplotsetmaincoords{75}{115}
%
\begin{tikzpicture}[tdplot_main_coords,scale=1.75]
    \pgfmathsetmacro{\aureo}{0.5 * (1.0 + sqrt(5.0))} % the golden number
    \pgfmathsetmacro{\unidad}{1.0}
    \coordinate (1) at (0,\aureo,1);
    \coordinate (2) at (0,-\aureo,1);
    \coordinate (3) at (0,-\aureo,-1);
    \coordinate (4) at (0,\aureo,-1);
    \coordinate (5) at (1,0,\aureo);
    \coordinate (6) at (-1,0,\aureo);
    \coordinate (7) at (-1,0,-\aureo);
 
 
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