TikZ and LaTeX books with discount

TikZ and LaTeX books with discount

June 7, 2025
【新刊案内】『TikZによるLaTeXグラフィックス』 – New TikZ book in Japanese

【新刊案内】『TikZによるLaTeXグラフィックス』 – New TikZ book in Japanese

November 13, 2024
LaTeX Cookbook second edition published

LaTeX Cookbook second edition published

March 30, 2024

Regular Tetrahedron

by Posted on

Edit and compile if you like:

\documentclass{article}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usepackage{ifthen}
\begin{document}
\newcommand{\tetrahedron}[3][(0,0,0)]{
\tdplotsetmaincoords{#2}{#3}
\begin{tikzpicture}[
maincolor/.style=cyan,
scale=1.5,
tdplot_main_coords,
axis/.style={-stealth},
mainline/.style={maincolor,thick},
invisibleline/.style={cyan,densely dashed},
]
% axis
\draw[axis](-1.5,0,0)--(1.5,0,0)node[pos=1.1]{$x$};
\draw[axis](0,-1.5,0)--(0,1.5,0)node[pos=1.1]{$y$};
\draw[axis](0,0,-1)--(0,0,2)node[pos=1.1]{$z$};

% vertices
\coordinate[shift={#1}] (A) at (60:1);
\coordinate[shift={#1}] (B) at (180:1);
\coordinate[shift={#1}] (C) at (300:1);
\coordinate[shift={#1}] (O) at (0,0,{sqrt(2)});

% fill faces
\fill[maincolor,opacity=0.1](A)--(B)--(C)--cycle;
\fill[maincolor,opacity=0.1](O)--(B)--(C)--cycle;
\fill[maincolor,opacity=0.1](A)--(O)--(C)--cycle;
\fill[maincolor,opacity=0.1](A)--(B)--(O)--cycle;

% inner product
\pgfmathparse{-sin(\tdplotmaintheta)*sin(\tdplotmainphi)+(1+cos(60))*sin(\tdplotmaintheta)*cos(\tdplotmainphi)/sin(60)+cos(\tdplotmaintheta)/sqrt(2)>0}
\pgfmathsetmacro{\OBCprod}{\pgfmathresult}
\pgfmathparse{-sin(\tdplotmaintheta)*sin(\tdplotmainphi)-(1+cos(60))*sin(\tdplotmaintheta)*cos(\tdplotmainphi)/sin(60)+cos(\tdplotmaintheta)/sqrt(2)>0}
\pgfmathsetmacro{\OABprod}{\pgfmathresult}
\pgfmathparse{sin(\tdplotmaintheta)*sin(\tdplotmainphi)/cos(60)+cos(\tdplotmaintheta)/sqrt(2)>0}
\pgfmathsetmacro{\OCAprod}{\pgfmathresult}
\pgfmathparse{-cos(\tdplotmaintheta)>0}
\pgfmathsetmacro{\ABCprod}{\pgfmathresult}

\ifthenelse{\ABCprod=0 \and \OABprod=0 \and \OBCprod=0 \and \OCAprod=1}{
\draw[invisibleline](O)--(B) (A)--(B) (C)--(B); \draw[mainline](A)--(O)--(C)--cycle; % 0001
}{
\ifthenelse{\ABCprod=0 \and \OABprod=0 \and \OBCprod=1 \and \OCAprod=0}{
\draw[invisibleline](O)--(A) (B)--(A) (C)--(A); \draw[mainline](O)--(B)--(C)--cycle; % 0010
}{
\ifthenelse{\ABCprod=0 \and \OABprod=0 \and \OBCprod=1 \and \OCAprod=1}{
\draw[mainline](O)--(C) (O)--(A)--(C) (O)--(B)--(C);\draw[invisibleline](A)--(B); % 0011
}{
\ifthenelse{\ABCprod=0 \and \OABprod=1 \and \OBCprod=0 \and \OCAprod=0}{
\draw[invisibleline](O)--(C) (A)--(C) (C)--(B); \draw[mainline](A)--(B)--(O)--cycle; % 0100
}{
\ifthenelse{\ABCprod=0 \and \OABprod=1 \and \OBCprod=0 \and \OCAprod=1}{
\draw[mainline](O)--(A) (O)--(B)--(A) (O)--(C)--(A);\draw[invisibleline](B)--(C); % 0101
}{
\ifthenelse{\ABCprod=0 \and \OABprod=1 \and \OBCprod=1 \and \OCAprod=0}{
\draw[mainline](O)--(B) (O)--(A)--(B) (O)--(C)--(B);\draw[invisibleline](A)--(C); % 0110
}{
\ifthenelse{\ABCprod=0 \and \OABprod=1 \and \OBCprod=1 \and \OCAprod=1}{
\draw[mainline](O)--(A) (O)--(B) (O)--(C) (A)--(B)--(C)--cycle; % 0111
}{
\ifthenelse{\ABCprod=1 \and \OABprod=0 \and \OBCprod=0 \and \OCAprod=0}{
\draw[invisibleline](O)--(A) (O)--(B) (O)--(C); \draw[mainline](A)--(B)--(C)--cycle; % 1000
}{
\ifthenelse{\ABCprod=1 \and \OABprod=0 \and \OBCprod=0 \and \OCAprod=1}{
\draw[mainline](A)--(C) (A)--(O)--(C) (A)--(B)--(C);\draw[invisibleline](O)--(B); % 1001
}{
\ifthenelse{\ABCprod=1 \and \OABprod=0 \and \OBCprod=1 \and \OCAprod=0}{
\draw[mainline](B)--(C) (B)--(A)--(C) (B)--(O)--(C);\draw[invisibleline](A)--(O); % 1010
}{
\ifthenelse{\ABCprod=1 \and \OABprod=0 \and \OBCprod=1 \and \OCAprod=1}{
\draw[mainline](O)--(A) (O)--(B) (O)--(C) (A)--(B)--(C)--cycle; % 1011
}{
\ifthenelse{\ABCprod=1 \and \OABprod=1 \and \OBCprod=0 \and \OCAprod=0}{
\draw[mainline](A)--(B) (A)--(C)--(B) (A)--(O)--(B);\draw[invisibleline](C)--(O); % 1100
}{
\ifthenelse{\ABCprod=1 \and \OABprod=1 \and \OBCprod=0 \and \OCAprod=1}{
\draw[mainline](O)--(A) (O)--(B) (O)--(C) (A)--(B)--(C)--cycle; % 1101
}{
\ifthenelse{\ABCprod=1 \and \OABprod=1 \and \OBCprod=1 \and \OCAprod=0}{
\draw[mainline](O)--(A) (O)--(B) (O)--(C) (A)--(B)--(C)--cycle; % 1110
}{%
}}}}}}}}}}}}}}

% draw points
\foreach \P in{A,B,C,O}
\path(0,0,{sqrt(2)/3})--(\P)node[pos=1.2]{\P};
\end{tikzpicture}
}

\tetrahedron{60}{35}

\end{document}

Edit and compile if you like:

\documentclass{article}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usepackage{ifthen}
\usepackage{tcolorbox}
\tcbuselibrary{most}
\usepackage[top=30truemm,bottom=30truemm,left=17truemm,right=17truemm]{geometry}

\begin{document}
\newcommand{\tetrahedron}[3][(0,0,0)]{
\tdplotsetmaincoords{#2}{#3}
\begin{tikzpicture}[
maincolor/.style=cyan,
scale=1.5,
tdplot_main_coords,
axis/.style={-stealth},
mainline/.style={maincolor,thick},
invisibleline/.style={cyan,densely dashed},
]
% axis
\draw[axis](-1.5,0,0)--(1.5,0,0)node[pos=1.1]{$x$};
\draw[axis](0,-1.5,0)--(0,1.5,0)node[pos=1.1]{$y$};
\draw[axis](0,0,-1)--(0,0,2)node[pos=1.1]{$z$};

% vertices
\coordinate[shift={#1}] (A) at (60:1);
\coordinate[shift={#1}] (B) at (180:1);
\coordinate[shift={#1}] (C) at (300:1);
\coordinate[shift={#1}] (O) at (0,0,{sqrt(2)});

% fill faces
\fill[maincolor,opacity=0.1](A)--(B)--(C)--cycle;
\fill[maincolor,opacity=0.1](O)--(B)--(C)--cycle;
\fill[maincolor,opacity=0.1](A)--(O)--(C)--cycle;
\fill[maincolor,opacity=0.1](A)--(B)--(O)--cycle;

% inner product
\pgfmathparse{-sin(\tdplotmaintheta)*sin(\tdplotmainphi)+(1+cos(60))*sin(\tdplotmaintheta)*cos(\tdplotmainphi)/sin(60)+cos(\tdplotmaintheta)/sqrt(2)>0}
\pgfmathsetmacro{\OBCprod}{\pgfmathresult}
\pgfmathparse{-sin(\tdplotmaintheta)*sin(\tdplotmainphi)-(1+cos(60))*sin(\tdplotmaintheta)*cos(\tdplotmainphi)/sin(60)+cos(\tdplotmaintheta)/sqrt(2)>0}
\pgfmathsetmacro{\OABprod}{\pgfmathresult}
\pgfmathparse{sin(\tdplotmaintheta)*sin(\tdplotmainphi)/cos(60)+cos(\tdplotmaintheta)/sqrt(2)>0}
\pgfmathsetmacro{\OCAprod}{\pgfmathresult}
\pgfmathparse{-cos(\tdplotmaintheta)>0}
\pgfmathsetmacro{\ABCprod}{\pgfmathresult}

\ifthenelse{\ABCprod=0 \and \OABprod=0 \and \OBCprod=0 \and \OCAprod=1}{
\draw[invisibleline](O)--(B) (A)--(B) (C)--(B); \draw[mainline](A)--(O)--(C)--cycle; % 0001
}{
\ifthenelse{\ABCprod=0 \and \OABprod=0 \and \OBCprod=1 \and \OCAprod=0}{
\draw[invisibleline](O)--(A) (B)--(A) (C)--(A); \draw[mainline](O)--(B)--(C)--cycle; % 0010
}{
\ifthenelse{\ABCprod=0 \and \OABprod=0 \and \OBCprod=1 \and \OCAprod=1}{
\draw[mainline](O)--(C) (O)--(A)--(C) (O)--(B)--(C);\draw[invisibleline](A)--(B); % 0011
}{
\ifthenelse{\ABCprod=0 \and \OABprod=1 \and \OBCprod=0 \and \OCAprod=0}{
\draw[invisibleline](O)--(C) (A)--(C) (C)--(B); \draw[mainline](A)--(B)--(O)--cycle; % 0100
}{
\ifthenelse{\ABCprod=0 \and \OABprod=1 \and \OBCprod=0 \and \OCAprod=1}{
\draw[mainline](O)--(A) (O)--(B)--(A) (O)--(C)--(A);\draw[invisibleline](B)--(C); % 0101
}{
\ifthenelse{\ABCprod=0 \and \OABprod=1 \and \OBCprod=1 \and \OCAprod=0}{
\draw[mainline](O)--(B) (O)--(A)--(B) (O)--(C)--(B);\draw[invisibleline](A)--(C); % 0110
}{
\ifthenelse{\ABCprod=0 \and \OABprod=1 \and \OBCprod=1 \and \OCAprod=1}{
\draw[mainline](O)--(A) (O)--(B) (O)--(C) (A)--(B)--(C)--cycle; % 0111
}{
\ifthenelse{\ABCprod=1 \and \OABprod=0 \and \OBCprod=0 \and \OCAprod=0}{
\draw[invisibleline](O)--(A) (O)--(B) (O)--(C); \draw[mainline](A)--(B)--(C)--cycle; % 1000
}{
\ifthenelse{\ABCprod=1 \and \OABprod=0 \and \OBCprod=0 \and \OCAprod=1}{
\draw[mainline](A)--(C) (A)--(O)--(C) (A)--(B)--(C);\draw[invisibleline](O)--(B); % 1001
}{
\ifthenelse{\ABCprod=1 \and \OABprod=0 \and \OBCprod=1 \and \OCAprod=0}{
\draw[mainline](B)--(C) (B)--(A)--(C) (B)--(O)--(C);\draw[invisibleline](A)--(O); % 1010
}{
\ifthenelse{\ABCprod=1 \and \OABprod=0 \and \OBCprod=1 \and \OCAprod=1}{
\draw[mainline](O)--(A) (O)--(B) (O)--(C) (A)--(B)--(C)--cycle; % 1011
}{
\ifthenelse{\ABCprod=1 \and \OABprod=1 \and \OBCprod=0 \and \OCAprod=0}{
\draw[mainline](A)--(B) (A)--(C)--(B) (A)--(O)--(B);\draw[invisibleline](C)--(O); % 1100
}{
\ifthenelse{\ABCprod=1 \and \OABprod=1 \and \OBCprod=0 \and \OCAprod=1}{
\draw[mainline](O)--(A) (O)--(B) (O)--(C) (A)--(B)--(C)--cycle; % 1101
}{
\ifthenelse{\ABCprod=1 \and \OABprod=1 \and \OBCprod=1 \and \OCAprod=0}{
\draw[mainline](O)--(A) (O)--(B) (O)--(C) (A)--(B)--(C)--cycle; % 1110
}{%
}}}}}}}}}}}}}}

% draw points
\foreach \P in{A,B,C,O}
\path(0,0,{sqrt(2)/3})--(\P)node[pos=1.2]{\P};
\end{tikzpicture}
}

\begin{tcbitemize}[
    raster equal height=rows,
    raster columns=3,
    colframe=black!70!blue,
    colback=white,
    sharp corners,
    ]
\tcbitem[title={\centering$\theta=60,\phi=35$}]\centering
\tetrahedron{60}{35}

\tcbitem[title={\centering$\theta=60,\phi=80$}]\centering
\tetrahedron{60}{80}

\tcbitem[title={\centering$\theta=60,\phi=120$}]\centering
\tetrahedron{60}{120}

\tcbitem[title={\centering$\theta=60,\phi=35$}]\centering
\tetrahedron{30}{35}

\tcbitem[title={\centering$\theta=60,\phi=80$}]\centering
\tetrahedron{20}{80}

\tcbitem[title={\centering$\theta=60,\phi=120$}]\centering
\tetrahedron{30}{120}
\end{tcbitemize}

\end{document}