Edit and compile if you like:
\documentclass{article}
\usepackage{tikz}
%\usetikzlibrary{patterns}
%\usetikzlibrary{math}
\usepackage{tikz-3dplot}
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{0.125pt}
%
% File name: diminished-hexagonal-trapezohedron.tex
% Description:
% A geometric representation of the diminished hexagonal trapezohedron is shown.
%
% Date of creation: July, 07th, 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 481 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{70}{115}
%
\begin{tikzpicture}[tdplot_main_coords]
% Change the value of the number at {\escala}{##} to scale the figure up or down
\pgfmathsetmacro{\escala}{2.0}
\pgfmathsetmacro{\r}{\escala}
\pgfmathsetmacro{\cero}{sqrt(2.0 * (3.0 * sqrt(3.0) - 5.0)) / 4.0}
\pgfmathsetmacro{\uno}{sqrt(3.0) / 2.0}
\pgfmathsetmacro{\dos}{sqrt(2.0 * (19.0 + 11.0 * sqrt(3.0))) / 4.0}
% Coordinates of the vertices
\coordinate(1) at (\escala*0.0,\escala*0.0,\escala*\dos);
\coordinate(2) at (\escala*0.0, \escala*0.0, -\escala*\dos);
\coordinate(3) at (\escala*0.0, \escala*1.0, \escala*\cero);
\coordinate(4) at (\escala*0.0, -\escala*1.0, \escala*\cero);
\coordinate(5) at (\escala*1.0, \escala*0.0, -\escala*\cero);
\coordinate(6) at (-\escala*1.0, \escala*0.0, -\escala*\cero);
\coordinate(7) at (\escala*\uno, \escala*0.5, \escala*\cero);
\coordinate(8) at (\escala*\uno, -\escala*0.5, \escala*\cero);
\coordinate(9) at (-\escala*\uno, \escala*0.5, \escala*\cero);
\coordinate(10) at (-\escala*\uno, -\escala*0.5, \escala*\cero);
%
\coordinate(11) at (\escala*0.5, \escala*\uno, -\escala*\cero);
\coordinate(12) at (\escala*0.5, -\escala*\uno, -\escala*\cero);
\coordinate(13) at (-\escala*0.5, \escala*\uno, -\escala*\cero);
\coordinate(14) at (-\escala*0.5, -\escala*\uno, -\escala*\cero);
% Faces of the polyhedron
% Hexagonal face
\draw[red,thick,fill=cyan!35,opacity=0.75] (13) -- (11) -- (5) -- (12) -- (14) -- (6) -- cycle;
% Triangular faces (back)
\draw[red,thick,fill=cyan!35,opacity=0.75] (12) -- (4) -- (14) -- cycle;
\draw[red,thick,fill=cyan!35,opacity=0.75] (14) -- (10) -- (6) -- cycle;
\draw[red,thick,fill=cyan!35,opacity=0.75] (6) -- (9) -- (13) -- cycle;
% Deltoids (back)
\draw[red,thick,fill=cyan!35,opacity=0.75] (1) -- (9) -- (6) -- (10) -- cycle;
\draw[red,thick,fill=cyan!35,opacity=0.75] (1) -- (10) -- (14) -- (4) -- cycle;
\draw[red,thick,fill=cyan!35,opacity=0.75] (1) -- (3) -- (13) -- (9) -- cycle;
% More deltoids (front)
\draw[red,thick,fill=cyan!35,opacity=0.75] (1) -- (4) -- (12) -- (8) -- cycle;
\draw[red,thick,fill=cyan!35,opacity=0.75] (1) -- (8) -- (5) -- (7) -- cycle;
\draw[red,thick,fill=cyan!35,opacity=0.75] (1) -- (7) -- (11) -- (3) -- cycle;
% More triangular faces (front)
\draw[red,thick,fill=cyan!35,opacity=0.75] (3) -- (11) -- (13) -- cycle;
\draw[red,thick,fill=cyan!35,opacity=0.75] (11) -- (7) -- (5) -- cycle;
\draw[red,thick,fill=cyan!35,opacity=0.75] (5) -- (8) -- (12) -- cycle;
%
\end{tikzpicture}
%
\end{document}
Click to download: diminished-hexagonal-trapezohedron.tex • diminished-hexagonal-trapezohedron.pdf
Open in Overleaf: diminished-hexagonal-trapezohedron.tex
See more on the author page of Efraín Soto Apolinar.
It took me around 2 hours to get here.
I was looking for a name of the shape used in the game IQ Six Pro
https://www.smartgames.eu/uk/one-player-games/iq-six-pro
and I believe this is the closest one I found.
a Elongated hexagonal trapezohedron with the code
“`
\documentclass{article}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{0.125pt}
%
% File name: elongated-hexagonal-trapezohedron.tex
% Description:
% A geometric representation of the elongated hexagonal trapezohedron:
% a hexagonal trapezohedron (12 kites) cut along its zigzag equator,
% with a belt of 6 hexagons inserted between the two 6-kite caps.
% 18 faces (12 kites + 6 hexagons), 42 edges, 26 vertices.
%
% Style based on the diminished-hexagonal-trapezohedron figure by
% Efrain Soto Apolinar (aprendematematicas.org.mx / TikZ.net).
%
\begin{document}
\tdplotsetmaincoords{70}{115}
%
\begin{tikzpicture}[tdplot_main_coords]
% Change the value of \escala to scale the figure up or down
\pgfmathsetmacro{\escala}{3.0}
% Shape parameters (tweak freely):
\pgfmathsetmacro{\za}{1.0} % apex height H
\pgfmathsetmacro{\zt}{0.4} % belt half-height t (hexagon tip ring)
% Derived values (do not change: they keep all faces planar):
\pgfmathsetmacro{\zu}{0.25*\za + 0.75*\zt} % kite-ring height u = H/4 + 3t/4
\pgfmathsetmacro{\rt}{1.0} % radius of hexagon-tip rings (T,S)
\pgfmathsetmacro{\ru}{sqrt(3)/2} % radius of kite rings (U,D) = (sqrt(3)/2)*rt
% Apexes
\coordinate (A) at (0,0,{\escala*\za});
\coordinate (B) at (0,0,{-\escala*\za});
% Rings of vertices:
% U = upper kite ring, T = upper belt tips, S = lower belt tips, D = lower kite ring
\foreach \k in {0,1,2,3,4,5}{%
\pgfmathsetmacro{\angU}{60*\k}
\pgfmathsetmacro{\angT}{60*\k + 30}
\coordinate (U\k) at ({\escala*\ru*cos(\angU)},{\escala*\ru*sin(\angU)},{\escala*\zu});
\coordinate (D\k) at ({\escala*\ru*cos(\angU)},{\escala*\ru*sin(\angU)},{-\escala*\zu});
\coordinate (T\k) at ({\escala*\rt*cos(\angT)},{\escala*\rt*sin(\angT)},{\escala*\zt});
\coordinate (S\k) at ({\escala*\rt*cos(\angT)},{\escala*\rt*sin(\angT)},{-\escala*\zt});
}
% Faces of the polyhedron
% Belt hexagons (back)
\draw[red,thick,fill=cyan!35,opacity=0.75] (T2) — (U3) — (T3) — (S3) — (D3) — (S2) — cycle;
\draw[red,thick,fill=cyan!35,opacity=0.75] (T1) — (U2) — (T2) — (S2) — (D2) — (S1) — cycle;
\draw[red,thick,fill=cyan!35,opacity=0.75] (T3) — (U4) — (T4) — (S4) — (D4) — (S3) — cycle;
% Bottom kites (back)
\draw[red,thick,fill=cyan!35,opacity=0.75] (B) — (D2) — (S2) — (D3) — cycle;
\draw[red,thick,fill=cyan!35,opacity=0.75] (B) — (D3) — (S3) — (D4) — cycle;
\draw[red,thick,fill=cyan!35,opacity=0.75] (B) — (D1) — (S1) — (D2) — cycle;
\draw[red,thick,fill=cyan!35,opacity=0.75] (B) — (D4) — (S4) — (D5) — cycle;
% Top kites (back)
\draw[red,thick,fill=cyan!35,opacity=0.75] (A) — (U2) — (T2) — (U3) — cycle;
\draw[red,thick,fill=cyan!35,opacity=0.75] (A) — (U3) — (T3) — (U4) — cycle;
\draw[red,thick,fill=cyan!35,opacity=0.75] (A) — (U1) — (T1) — (U2) — cycle;
\draw[red,thick,fill=cyan!35,opacity=0.75] (A) — (U4) — (T4) — (U5) — cycle;
% Bottom kites (front)
\draw[red,thick,fill=cyan!35,opacity=0.75] (B) — (D5) — (S5) — (D0) — cycle;
\draw[red,thick,fill=cyan!35,opacity=0.75] (B) — (D0) — (S0) — (D1) — cycle;
% Belt hexagons (front)
\draw[red,thick,fill=cyan!35,opacity=0.75] (T4) — (U5) — (T5) — (S5) — (D5) — (S4) — cycle;
\draw[red,thick,fill=cyan!35,opacity=0.75] (T0) — (U1) — (T1) — (S1) — (D1) — (S0) — cycle;
\draw[red,thick,fill=cyan!35,opacity=0.75] (T5) — (U0) — (T0) — (S0) — (D0) — (S5) — cycle;
% Top kites (front)
\draw[red,thick,fill=cyan!35,opacity=0.75] (A) — (U5) — (T5) — (U0) — cycle;
\draw[red,thick,fill=cyan!35,opacity=0.75] (A) — (U0) — (T0) — (U1) — cycle;
%
\end{tikzpicture}
%
\end{document}
“`