\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);
	\coordinate(4) at (\escala*\uno, \escala*0.0, \escala*0.5);
	\coordinate(5) at (\escala*\uno, \escala*0.0, -\escala*0.5);
	\coordinate(6) at (-\escala*\uno, \escala*0.0, \escala*0.5);
	\coordinate(7) at (-\escala*\uno, \escala*0.0, -\escala*0.5);
	\coordinate(8) at (\escala*0.5, \escala*\uno, \escala*0.0);
	\coordinate(9) at (\escala*0.5, -\escala*\uno, \escala*0.0);
	\coordinate(10) at (-\escala*0.5, \escala*\uno, \escala*0.0);
	%
	\coordinate(11) at (-\escala*0.5, -\escala*\uno, \escala*0.0);
	\coordinate(12) at (\escala*\cero, \escala*\cero, \escala*\cero);
	\coordinate(13) at (\escala*\cero, \escala*\cero, -\escala*\cero);
	\coordinate(14) at (\escala*\cero, -\escala*\cero, \escala*\cero);
	\coordinate(15) at (\escala*\cero, -\escala*\cero, -\escala*\cero);
	\coordinate(16) at (-\escala*\cero, \escala*\cero, \escala*\cero);
	\coordinate(17) at (-\escala*\cero, \escala*\cero, -\escala*\cero);
	\coordinate(18) at (-\escala*\cero, -\escala*\cero, \escala*\cero);
	\coordinate(19) at (-\escala*\cero, -\escala*\cero, -\escala*\cero);
	% 
	\coordinate (20) at ($(4)!+\aureo!(6)$);
	\coordinate (21) at ($(6)!+\aureo!(4)$);
	\coordinate (22) at ($(0)!+\aureo!(1)$);
	\coordinate (23) at ($(0)!+\aureo!(15)$);
	\coordinate (24) at ($(16)!+\aureo!(3)$);
	\coordinate (25) at ($(2)!+\aureo!(3)$);
	\coordinate (26) at ($(1)!+\aureo!(18)$);
	\coordinate (27) at ($(1)!+\aureo!(0)$);
	\coordinate (28) at ($(2)!+\aureo!(17)$);
	\coordinate (29) at ($(3)!+\aureo!(2)$);
	\coordinate (30) at ($(12)!+\aureo!(3)$);
	\coordinate (31) at ($(2)!+\aureo!(13)$);
	% Faces of the polyhedron
	\draw[red,thick,fill=cyan!35,opacity=0.75] (31) -- (4) -- (5);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (31) -- (5) -- (13);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (31) -- (13) -- (8);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (31) -- (8) -- (12);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (31) -- (12) -- (4);
	%
	\draw[red,thick,fill=cyan!35,opacity=0.75] (30) -- (1) -- (3);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (30) -- (3) -- (15);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (30) -- (15) -- (5);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (30) -- (13) -- (1);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (30) -- (5) -- (13);
	%
	\draw[red,thick,fill=cyan!35,opacity=0.75] (23) -- (4) -- (5);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (23) -- (5) -- (15);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (23) -- (15) -- (9);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (23) -- (9) -- (14);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (23) -- (14) -- (4);
	%
	\draw[red,thick,fill=cyan!35,opacity=0.75] (21) -- (14) -- (4);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (21) -- (0) -- (2);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (21) -- (2) -- (14);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (21) -- (4) -- (12);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (21) -- (12) -- (0);
	%
	\draw[red,thick,fill=cyan!35,opacity=0.75] (22) -- (10) -- (17);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (22) -- (17) -- (1);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (22) -- (1) -- (13);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (22) -- (8) -- (10);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (22) -- (13) -- (8);
	%
	\draw[red,thick,fill=cyan!35,opacity=0.75] (27) -- (12) -- (8);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (27) -- (8) -- (10);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (27) -- (10) -- (16);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (27) -- (16) -- (0);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (27) -- (0) -- (12);
	%
	\draw[red,thick,fill=cyan!35,opacity=0.75] (24) -- (1) -- (3);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (24) -- (3) -- (19);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (24) -- (19) -- (7);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (24) -- (17) -- (1);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (24) -- (7) -- (17);
	%
	\draw[red,thick,fill=cyan!35,opacity=0.75] (29) -- (2) -- (14);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (29) -- (14) -- (9);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (29) -- (9) -- (11);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (29) -- (18) -- (2);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (29) -- (11) -- (18);
	%
	\draw[red,thick,fill=cyan!35,opacity=0.75] (25) -- (3) -- (15);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (25) -- (15) -- (9);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (25) -- (9) -- (11);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (25) -- (11) -- (19);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (25) -- (19) -- (3);
	%
	\draw[red,thick,fill=cyan!35,opacity=0.75] (20) -- (0) -- (2);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (20) -- (2) -- (18);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (20) -- (16) -- (0);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (20) -- (6) -- (16);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (20) -- (18) -- (6);
	%
	\draw[red,thick,fill=cyan!35,opacity=0.75] (28) -- (7) -- (6);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (28) -- (16) -- (10);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (28) -- (10) -- (17);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (28) -- (17) -- (7);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (28) -- (6) -- (16);	
	%
	\draw[red,thick,fill=cyan!35,opacity=0.75] (26) -- (6) -- (7);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (26) -- (7) -- (19);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (26) -- (19) -- (11);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (26) -- (11) -- (18);
	\draw[red,thick,fill=cyan!35,opacity=0.75] (26) -- (18) -- (6);
	%
	\end{tikzpicture}
	%
\end{document}
