Rhombic Hexecontahedron

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\documentclass{article}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{0.125pt}
%
% File name: rhombic-hexecontahedron.tex
% Description: 
% A geometric representation of the rhombic hexecontahedron is shown.
% 
% Date of creation: June, 30th, 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 227 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}
\tdplotsetmaincoords{80}{30}
%
\begin{tikzpicture}[tdplot_main_coords]
    % Change the value of the number at {\escala}{##} to scale the figure up or down
    \pgfmathsetmacro{\escala}{1.25}
    \pgfmathsetmacro{\r}{\escala}
    % Coordinates of the vertices
    \coordinate(1) at (-\escala*2.34164, \escala*0., -\escala*0.447214);
    \coordinate(2) at (-\escala*1.89443, -\escala*1.37638, \escala*0.447214);
    \coordinate(3) at (-\escala*1.89443, \escala*1.37638, \escala*0.447214);
    \coordinate(4) at (-\escala*1.61803, -\escala*0.525731, \escala*0.);
    \coordinate(5) at (-\escala*1.61803, \escala*0.525731, \escala*0.);
    \coordinate(6) at (-\escala*1.44721, \escala*0., -\escala*1.89443);
    \coordinate(7) at (-\escala*1.44721, \escala*0., -\escala*0.894427);
    \coordinate(8) at (-\escala*1.17082, -\escala*0.850651, \escala*0.894427);
    \coordinate(9) at (-\escala*1.17082, -\escala*0.850651, \escala*1.89443);
 
 
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