\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{patterns}
%\usetikzlibrary{math}
\usepackage{tikz-3dplot}
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{0.125pt}
%
% File name: heptagonal-trapezohedron.tex
% Description: 
% A geometric representation of the heptagonal trapezohedron is shown.
% 
% Date of creation: June, 27th, 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 482 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}{130}
%
\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}
	\pgfmathsetmacro{\cero}{0.153192768}
	\pgfmathsetmacro{\uno}{0.25642921}
	\pgfmathsetmacro{\dos}{0.7184986963}
	\pgfmathsetmacro{\tres}{0.9009688679}
	\pgfmathsetmacro{\cuatro}{1.03826}
	\pgfmathsetmacro{\cinco}{1.1234898}
	\pgfmathsetmacro{\seis}{1.15238243548}
	\pgfmathsetmacro{\siete}{2.9406377276}
	% Coordinates of the vertices
	\coordinate(1) at (\escala*0.0, \escala*0.0, \escala*\siete);
	\coordinate(2) at (\escala*0.0, \escala*0.0, -\escala*\siete);
	\coordinate(3) at (\escala*\cinco, \escala*\uno, \escala*\cero);
	\coordinate(4) at (\escala*\cinco, -\escala*\uno, -\escala*\cero);
	\coordinate(5) at (-\escala*\cinco, \escala*\uno, \escala*\cero);
	\coordinate(6) at (-\escala*\cinco, -\escala*\uno, -\escala*\cero);
	\coordinate(7) at (\escala*\tres, -\escala*\dos, \escala*\cero);
	\coordinate(8) at (\escala*\tres, \escala*\dos, -\escala*\cero);
	\coordinate(9) at (-\escala*\tres, -\escala*\dos, \escala*\cero);
	\coordinate(10) at (-\escala*\tres, \escala*\dos, -\escala*\cero);
	%
	\coordinate(11) at (\escala*0.5, \escala*\cuatro, \escala*\cero);
	\coordinate(12) at (\escala*0.5, -\escala*\cuatro, -\escala*\cero);
	\coordinate(13) at (-\escala*0.5, \escala*\cuatro, \escala*\cero);
	\coordinate(14) at (-\escala*0.5, -\escala*\cuatro, -\escala*\cero);
	\coordinate(15) at (\escala*0.0, -\escala*\seis, \escala*\cero);
	\coordinate(16) at (\escala*0.0, \escala*\seis, -\escala*\cero);
	% Faces of the polyhedron
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (1) -- (3) -- (8) -- (11) -- cycle;
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (1) -- (7) -- (4) -- (3) -- cycle;
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (2) -- (16) -- (11) -- (8) -- cycle;
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (2) -- (8) -- (3) -- (4) -- cycle;
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (2) -- (4) -- (7) -- (12) -- cycle;
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (1) -- (15) -- (12) -- (7) -- cycle;
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (1) -- (11) -- (16) -- (13) -- cycle;
	%
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (2) -- (10) -- (13) -- (16) -- cycle;
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (2) -- (6) -- (5) -- (10) -- cycle;
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (1) -- (5) -- (6) -- (9) -- cycle;
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (1) -- (13) -- (10) -- (5) -- cycle;
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (2) -- (14) -- (9) -- (6) -- cycle;
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (2) -- (12) -- (15) -- (14) -- cycle;
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (1) -- (9) -- (14) -- (15) -- cycle;
	%
	\end{tikzpicture}
	%
\end{document}



