Excavated Dodecahedron

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\documentclass{article}
\usepackage{tikz}
%\usetikzlibrary{patterns}
%\usetikzlibrary{math}
\usepackage{tikz-3dplot}
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{0.125pt}
%
% File name: excavated-dodecahedron.tex
% Description: 
% A geometric representation of the excavated dodecahedron is shown.
% 
% Date of creation: July, 22nd, 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 140 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}{120}
%
\begin{tikzpicture}[tdplot_main_coords]
    % Change the value of the number at {\escala}{##} to scale the figure up or down
    \pgfmathsetmacro{\escala}{1.85}
    \pgfmathsetmacro{\r}{\escala}
    \pgfmathsetmacro{\cero}{(1.0 + sqrt(5.0)) / 4.0}
    \pgfmathsetmacro{\uno}{(3.0 + sqrt(5.0)) / 4.0}
    \pgfmathsetmacro{\aureo}{2.0 / (1.0 + sqrt(5.0))}
    % Coordinates of the vertices
    \coordinate(0) at (\escala*0.0, \escala*0.5, \escala*\uno);
    \coordinate(1) at (\escala*0.0, \escala*0.5, -\escala*\uno);
    \coordinate(2) at (\escala*0.0, -\escala*0.5, \escala*\uno);
    \coordinate(3) at (\escala*0.0, -\escala*0.5, -\escala*\uno);
 
 
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