# Rhombic Dodecahedron and Escher Solid

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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: rhombic-dodecahedron-and-escher-solid.tex
% Description:
% A geometric representation of the construction of an
% escher-solid as the stellation of a rhombic dodecahedron is shown.
%
% Date of last modification: October, 9th, 2022.
% Author: Efraín Soto Apolinar.
% https://www.aprendematematicas.org.mx/author/efrain-soto-apolinar/instructing-courses/
% Source: page 175 of the
% Glosario Ilustrado de Matem\'aticas Escolares.
% https://tinyurl.com/5udm2ufy
%
% According to TikZ.net
%
\begin{document}
\tdplotsetmaincoords{80}{115}
%
\begin{tikzpicture}[tdplot_main_coords]
% Change the value of the number at {\arista}{##} to scale the figure up or down
\pgfmathsetmacro{\arista}{2.25}
% Coordinates of the vertices
\coordinate (1) at (\arista,-\arista,0);
\coordinate (2) at (\arista,\arista,0);
\coordinate (3) at (-\arista,\arista,0);
\coordinate (4) at (-\arista,-\arista,0);
\coordinate (5) at (\arista,0,\arista);
\coordinate (6) at (\arista,0,-\arista);
\coordinate (8) at (-\arista,0,\arista);
\coordinate (7) at (-\arista,0,-\arista);
\coordinate (9) at (0,\arista,\arista);
\coordinate (10) at (0,-\arista,\arista);
\coordinate (11) at (0,-\arista,-\arista);
\coordinate (12) at (0,\arista,-\arista);
\coordinate (13) at (\arista,0,0);
\coordinate (14) at (0,\arista,0);
\coordinate (15) at (-\arista,0,0);
\coordinate (16) at (0,-\arista,0);
\coordinate (17) at (0,0,\arista);
\coordinate (18) at (0,0,-\arista);
\coordinate (19) at (-0.5*\arista,0.5*\arista,0.5*\arista);
\coordinate (20) at (0.5*\arista,0.5*\arista,0.5*\arista);
\coordinate (21) at (-0.5*\arista,-0.5*\arista,0.5*\arista);
\coordinate (22) at (0.5*\arista,-0.5*\arista,0.5*\arista);
\coordinate (23) at (-0.5*\arista,0.5*\arista,-0.5*\arista);
\coordinate (24) at (0.5*\arista,0.5*\arista,-0.5*\arista);
\coordinate (25) at (-0.5*\arista,-0.5*\arista,-0.5*\arista);
\coordinate (26) at (0.5*\arista,-0.5*\arista,-0.5*\arista);
%
% Faces of the polyhedron
%
\draw[gray,thin]  (7) -- (15) -- (25) -- cycle;
\draw[gray,thin]  (7) -- (18) -- (25) -- cycle;
\draw[gray,thin]  (7) -- (15) -- (23) -- cycle;
\draw[gray,thin]  (7) -- (18) -- (23) -- cycle;
\draw[red,thick,fill=cyan!35,opacity=0.75] (15) -- (25) -- (18) -- (23) -- cycle;
%
\draw[gray,thin]  (4) -- (15) -- (25) -- cycle;
\draw[gray,thin]  (4) -- (15) -- (21) -- cycle;
\draw[gray,thin]  (4) -- (16) -- (21) -- cycle;
\draw[gray,thin]  (4) -- (16) -- (25) -- cycle;
\draw[red,thick,fill=cyan!35,opacity=0.75] (21) -- (16) -- (25) -- (15) -- cycle;
%
\draw[gray,thin]  (8) -- (15) -- (19) -- cycle;
\draw[gray,thin]  (8) -- (21) -- (15) -- cycle;
\draw[gray,thin]  (8) -- (17) -- (21) -- cycle;
\draw[gray,thin]  (8) -- (19) -- (17) -- cycle;
\draw[red,thick,fill=cyan!35,opacity=0.75] (17) -- (21) -- (15) -- (19) -- cycle;
%
\draw[gray,thin]  (10) -- (21) -- (17) -- cycle;
\draw[gray,thin]  (10) -- (16) -- (21) -- cycle;
\draw[gray,thin]  (10) -- (22) -- (16) -- cycle;
\draw[gray,thin]  (10) -- (17) -- (22) -- cycle;
\draw[red,thick,fill=cyan!35,opacity=0.75] (17) -- (22) -- (16) -- (21) -- cycle;
%
%
%
\draw[gray,thin]  (3) -- (15) -- (23) -- cycle;
\draw[gray,thin]  (3) -- (15) -- (19) -- cycle;
\draw[gray,thin]  (3) -- (14) -- (19) -- cycle;
\draw[gray,thin]  (3) -- (14) -- (23) -- cycle;
\draw[red,thick,fill=cyan!35,opacity=0.75] (19) -- (14) -- (23) -- (15) -- cycle;
%
\draw[gray,thin]  (11) -- (16) -- (25) -- cycle;
\draw[gray,thin]  (11) -- (18) -- (25) -- cycle;
\draw[gray,thin]  (11) -- (16) -- (26) -- cycle;
\draw[gray,thin]  (11) -- (18) -- (26) -- cycle;
\draw[red,thick,fill=cyan!35,opacity=0.75] (16) -- (26) -- (18) -- (25) -- cycle;
%
\draw[red,thick,fill=cyan!35,opacity=0.75] (22) -- (13) -- (26) -- (16) -- cycle;
\draw[gray,thin]  (1) -- (16) -- (26) -- cycle;
\draw[gray,thin]  (1) -- (13) -- (26) -- cycle;
\draw[gray,thin]  (1) -- (16) -- (22) -- cycle;
\draw[gray,thin]  (1) -- (13) -- (22) -- cycle;
%
\draw[red,thick,fill=cyan!35,opacity=0.75] (14) -- (23) -- (18) -- (24) -- cycle;
\draw[gray,thin]  (12) -- (14) -- (23) -- cycle;
\draw[gray,thin]  (12) -- (18) -- (23) -- cycle;
\draw[gray,thin]  (12) -- (18) -- (24) -- cycle;
\draw[gray,thin]  (12) -- (14) -- (24) -- cycle;
%
\draw[red,thick,fill=cyan!35,opacity=0.75] (17) -- (20) -- (14) -- (19) -- cycle;
\draw[gray,thin]  (9) -- (17) -- (19) -- cycle;
\draw[gray,thin]  (9) -- (19) -- (14) -- cycle;
\draw[gray,thin]  (9) -- (17) -- (20) -- cycle;
\draw[gray,thin]  (9) -- (14) -- (20) -- cycle;
%
\draw[red,thick,fill=cyan!35,opacity=0.75] (17) -- (20) -- (13) -- (22) -- cycle;
\draw[gray,thin]  (5) -- (22) -- (17) -- cycle;
\draw[gray,thin]  (5) -- (22) -- (13) -- cycle;
\draw[gray,thin]  (5) -- (13) -- (20) -- cycle;
\draw[gray,thin]  (5) -- (20) -- (17) -- cycle;
%
\draw[red,thick,fill=cyan!35,opacity=0.75] (13) -- (24) -- (18) -- (26) -- cycle;
\draw[gray,thin]  (6) -- (18) -- (26) -- cycle;
\draw[gray,thin]  (6) -- (13) -- (26) -- cycle;
\draw[gray,thin]  (6) -- (13) -- (24) -- cycle;
\draw[gray,thin]  (6) -- (18) -- (24) -- cycle;
%
\draw[red,thick,fill=cyan!35,opacity=0.75] (20) -- (14) -- (24) -- (13) -- cycle;
\draw[gray,thin]  (2) -- (14) -- (24) -- cycle;
\draw[gray,thin]  (2) -- (13) -- (24) -- cycle;
\draw[gray,thin]  (2) -- (13) -- (20) -- cycle;
\draw[gray,thin]  (2) -- (14) -- (20) -- cycle;
%
\end{tikzpicture}
%
\end{document}