Deltoidal Icositetrahedron

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\documentclass{article}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{0.125pt}
%
% File name: deltoidal-icositetrahedron.tex
% Description: 
% A geometric representation of a deltoidal icositetrahedron is shown.
% 
% Date of creation: May, 18th, 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 234 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}{140}
%
\begin{tikzpicture}[tdplot_main_coords]
    % Change the value of the number at {\escala}{##} to scale the figure up or down
    \pgfmathsetmacro{\escala}{1.5}
    % Coordinates of the vertices
    \coordinate(1) at (-\escala*1.19448, \escala* -1.19448, \escala* 0.);
    \coordinate(2) at (-\escala*1.19448, \escala* 0., \escala* -1.19448);
    \coordinate(3) at (-\escala*1.19448, \escala* 0., \escala* 1.19448);
    \coordinate(4) at (-\escala*1.19448, \escala* 1.19448, \escala* 0.);
    \coordinate(5) at (\escala*0., \escala* -1.19448, \escala* -1.19448);
    \coordinate(6) at (\escala*0., \escala* -1.19448, \escala* 1.19448);
    \coordinate(7) at (\escala*0., \escala* 0., \escala* -1.68925);
    \coordinate(8) at (\escala*0., \escala* 0., \escala* 1.68925);
    \coordinate(9) at (\escala*0., \escala* 1.19448, \escala* -1.19448);
    \coordinate(10) at (\escala*0., \escala* 1.19448, \escala* 1.19448);
 
 
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