\documentclass{article}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{0.125pt}
%
% File name: regular-hexagonal-toroid-24-faces.tex
% Description: 
% A geometric representation of the 
% regular hexagonal toroid with 24 faces is shown.
% 
% Date of creation: July, 08th, 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 476 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}{105}
%
\begin{tikzpicture}[tdplot_main_coords,scale=0.25]
	% Coordinates of the vertices
	\coordinate(0) at (-11, 5, 11);
	\coordinate(1) at (-11, -5, 11);
	\coordinate(2) at (11, -11, 5);
	\coordinate(3) at (11, -11, -5);
	\coordinate(4) at (5, 11, -11);
	\coordinate(5) at (-5, 11, -11);
	\coordinate(6) at (-7, 5, 11);
	\coordinate(7) at (11, -7, 5);
	\coordinate(8) at (5, 11, -7);
	\coordinate(9) at (-5, 7, -11);
	\coordinate(10) at (-11, -5, 7);
	%
	\coordinate(11) at (7, -11, -5);
	\coordinate(12) at (-7, -1, 11);
	\coordinate(13) at (11, -7, -1);
	\coordinate(14) at (-1, 11, -7);
	\coordinate(15) at (1, 7, -11);
	\coordinate(16) at (-11, 1, 7);
	\coordinate(17) at (7, -11, 1);
	\coordinate(18) at (5, -5, 11);
	\coordinate(19) at (5, -5, -11);
	\coordinate(20) at (11, 5, -5);
	%
	\coordinate(21) at (-11, 5, -5);
	\coordinate(22) at (-5, 11, 5);
	\coordinate(23) at (-5, -11, 5);
	\coordinate(24) at (5, -1, 11);
	\coordinate(25) at (11, 5, -1);
	\coordinate(26) at (-1, 11, 5);
	\coordinate(27) at (1, -5, -11);
	\coordinate(28) at (-11, 1, -5);
	\coordinate(29) at (-5, -11, 1);
	\coordinate(30) at (-7, 1, 7);
	%
	\coordinate(31) at (-7, -1, 7);
	\coordinate(32) at (7, -7, 1);
	\coordinate(33) at (7, -7, -1);
	\coordinate(34) at (1, 7, -7);
	\coordinate(35) at (-1, 7, -7);
	\coordinate(36) at (5, -1, -7);
	\coordinate(37) at (-7, 5, -1);
	\coordinate(38) at (-1, -7, 5);
	\coordinate(39) at (1, -5, 7);
	\coordinate(40) at (7, 1, -5);
	%
	\coordinate(41) at (-5, 7, 1);
	\coordinate(42) at (1, -1, 7);
	\coordinate(43) at (1, -1, -7);
	\coordinate(44) at (7, 1, -1);
	\coordinate(45) at (-7, 1, -1);
	\coordinate(46) at (-1, 7, 1);
	\coordinate(47) at (-1, -7, 1);
	% Faces of the polyhedron
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (0) -- (21) -- (28) -- (16) -- (10) -- (1) -- cycle;
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (30) -- (16) -- (28) -- (40) -- (44) -- (45) -- cycle;
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (30) -- (31) -- (42) -- (39) -- (10) -- (16) -- cycle;
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (30) -- (45) -- (37) -- (6) -- (12) -- (31) -- cycle;
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (3) -- (11) -- (40) -- (28) -- (21) -- (20) -- cycle;
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (0) -- (6) -- (37) -- (25) -- (20) -- (21) -- cycle;
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (46) -- (47) -- (32) -- (17) -- (29) -- (41) -- cycle;
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (22) -- (5) -- (9) -- (41) -- (29) -- (23) -- cycle;
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (3) -- (2) -- (23) -- (29) -- (17) -- (11) -- cycle;
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (22) -- (23) -- (2) -- (7) -- (38) -- (26) -- cycle;
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (46) -- (41) -- (9) -- (15) -- (34) -- (35) -- cycle;
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (46) -- (35) -- (14) -- (26) -- (38) -- (47) -- cycle;
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (19) -- (27) -- (15) -- (9) -- (5) -- (4) -- cycle;
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (19) -- (18) -- (1) -- (10) -- (39) -- (27) -- cycle;
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (43) -- (34) -- (15) -- (27) -- (39) -- (42) -- cycle;
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (43) -- (42) -- (31) -- (12) -- (24) -- (36) -- cycle;
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (43) -- (36) -- (8) -- (14) -- (35) -- (34) -- cycle;
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (19) -- (4) -- (8) -- (36) -- (24) -- (18) -- cycle;
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (33) -- (44) -- (40) -- (11) -- (17) -- (32) -- cycle;
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (33) -- (13) -- (25) -- (37) -- (45) -- (44) -- cycle;
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (3) -- (20) -- (25) -- (13) -- (7) -- (2) -- cycle;
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (22) -- (26) -- (14) -- (8) -- (4) -- (5) -- cycle;
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (0) -- (1) -- (18) -- (24) -- (12) -- (6) -- cycle;
	\draw[red,thick,fill=cyan!35,opacity=0.75]  (33) -- (32) -- (47) -- (38) -- (7) -- (13) -- cycle;
	%
	\end{tikzpicture}
	%
\end{document}



