\documentclass[12pt]{article}

\usepackage{tikz,tkz-euclide}
\usetikzlibrary{positioning}
\usetikzlibrary{patterns,fadings}
\usetkzobj{all}
\usepackage[utf8]{inputenc}
\usepackage[margin=2cm]{geometry}
\usetikzlibrary{arrows}
\usepackage{url}

\usepackage{pgf,tikz,pgfplots}
\pgfplotsset{compat=1.15}

\definecolor{luma-red}{rgb}{0.949019607843137, 0.400000000000000, 0.309803921568627}
\definecolor{luma-purple}{rgb}{0.576470588235294, 0.384313725490196, 0.600000000000000}
\definecolor{luma-blue}{rgb}{0.019607843137255, 0.647058823529412, 0.772549019607843}
\definecolor{luma-green}{rgb}{0.196078431372549, 0.643137254901961, 0.450980392156863}
\definecolor{luma-gold}{rgb}{0.976470588235294, 0.643137254901961, 0.329411764705882}

\usetikzlibrary{fadings,shapes.geometric}

\input{mirror.tex}
\setlength{\parindent}{0pt}

\newcommand{\foldpoint}[3]{
\draw (#1) circle (1pt);
\filldraw (#2) circle (1pt);
\draw[->,>=stealth,red] (#1) to[bend #3](#2);
}
\def\ptable{gray!50}


\begin{document}
\thispagestyle{empty}
\section*{Kuutio}
\def\orientation{1}
\input{orientation.tex}
Tehdään origamikuutio. Näissä ohjeissa käytetään paperia, jonka etupuoli on {\color{\pfront} punainen} ja takapuoli on {\color{\pback} sininen}. Paperia pidetään samankokoisella pöydällä, joka on {\color{\ptable}harmaa}.

\begin{tikzpicture}%\pgfmathsetseed{7}
\input{reverseclip.tex}
\input{coordinates.tex}
\def\orientation{1}
\input{orientation.tex}

%paper
\filldraw[\pfront] (a) -- (b) -- (c) -- (d) -- cycle;
%ready lines

\coordinate (p1) at (1,0);
\coordinate (q1) at (0,1);
\draw (p1) -- (q1);
\filldraw[\ptable] (p1)--(q1)--(a)--cycle;
\begin{scope}
\begin{pgfinterruptboundingbox}
\path [clip] (q1) -- (p1) -- (a) -- cycle [reverseclip];
\end{pgfinterruptboundingbox}
\filldraw[gray!40] (a)--(b)--(c)--(d)--cycle;
\end{scope}
\begin{scope}[mirror=(p1)--(q1)]
\draw (0.98,0.98) coordinate (ap);
\end{scope}

\filldraw[\pback,draw=black,opacity=0.5] (p1)--(q1)--(ap)--cycle;
\foldpoint{a}{ap}{left}

\draw[black,thin] (a)--(b)--(c)--(d)--cycle;
\end{tikzpicture}

Taita paperi puoliksi (2 kpl).

\begin{tikzpicture}
\input{reverseclip.tex}
\input{coordinates.tex}
\def\orientation{1}
\input{orientation.tex}

\filldraw[\pfront] (a) -- (b) -- (c) -- (d) -- cycle;
\filldraw[\ptable] (n)--(s)--(b)--(a)--cycle;
\filldraw[\pback] (n) --(s)--(c)--(d)--cycle;
\draw (n) -- (s);
\foldpoint{a}{d}{right}
\foldpoint{b}{c}{left}
\draw[black,thin] (a)--(b)--(c)--(d)--cycle;
\end{tikzpicture}
\begin{tikzpicture}
\input{reverseclip.tex}
\input{coordinates.tex}
\def\orientation{1}
\input{orientation.tex}

\filldraw[\pfront] (a) -- (b) -- (c) -- (d) -- cycle;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%ready lines
\draw[\stylea] (n)--(s);
\draw[\stylea] (w)--(e);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\draw[black,thin] (a)--(b)--(c)--(d)--cycle;
\end{tikzpicture}

Taita sivut äskettäin syntyneille taitoksille (4 kpl).

\begin{tikzpicture}
\input{reverseclip.tex}
\input{coordinates.tex}
\def\orientation{1}
\input{orientation.tex}

\filldraw[\pfront] (a) -- (b) -- (c) -- (d) -- cycle;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%ready lines
\draw[\stylea] (n)--(s);
\draw[\stylea] (w)--(e);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\filldraw[\ptable] (na)--(a)--(b)--(sb)--cycle;
\filldraw[\pback] (n)--(na)--(sb)--(s)--cycle;
\draw (n) -- (s);
\draw (na) -- (sb);
\foldpoint{a}{n}{right}
\foldpoint{b}{s}{left}
\draw[black,thin] (a)--(b)--(c)--(d)--cycle;
\end{tikzpicture}
\begin{tikzpicture}
\input{reverseclip.tex}
\input{coordinates.tex}
\def\orientation{1}
\input{orientation.tex}

\filldraw[\pfront] (a) -- (b) -- (c) -- (d) -- cycle;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%ready lines
\draw[\stylea] (n)--(s);
\draw[\stylea] (w)--(e);
\draw[\stylea] (na)--(sb);
\draw[\stylea] (nd)--(sc);
\draw[\stylea] (wc)--(eb);
\draw[\stylea] (wd)--(ea);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\draw[black,thin] (a)--(b)--(c)--(d)--cycle;
\end{tikzpicture}

Nurjalta puolelta: taita kulmaa diagonaalisesti ``3/4 verran'' (4 kpl).

\begin{tikzpicture}
\input{reverseclip.tex}
\input{coordinates.tex}
\def\orientation{0}
\input{orientation.tex}

\filldraw[\pfront] (a) -- (b) -- (c) -- (d) -- cycle;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%ready lines
\draw[\stylea] (n)--(s);
\draw[\stylea] (w)--(e);
\draw[\stylea] (na)--(sb);
\draw[\stylea] (nd)--(sc);
\draw[\stylea] (wc)--(eb);
\draw[\stylea] (wd)--(ea);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\filldraw[\ptable] (ea)--(sc)--(b)--cycle;
\filldraw[\pback] (ea)--(sc)--(-0.5,0.5)--cycle;
\draw (ea) -- (sc);
\draw (ea) -- (-0.5,0.5) --(sc);
\foldpoint{b}{-0.5,0.5}{right}
\draw[black,thin] (a)--(b)--(c)--(d)--cycle;
\end{tikzpicture}
\begin{tikzpicture}
\input{reverseclip.tex}
\input{coordinates.tex}
\def\orientation{1}
\input{orientation.tex}

\filldraw[\pfront] (a) -- (b) -- (c) -- (d) -- cycle;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%ready lines
\draw[\stylea] (n)--(s);
\draw[\stylea] (w)--(e);
\draw[\stylea] (na)--(sb);
\draw[\stylea] (nd)--(sc);
\draw[\stylea] (wc)--(eb);
\draw[\stylea] (wd)--(ea);
\draw[\styleb] (ea)--(sc);
\draw[\styleb] (sb)--(wd);
\draw[\styleb] (wc)--(na);
\draw[\styleb] (nd)--(eb);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\draw[black,thin] (a)--(b)--(c)--(d)--cycle;
\end{tikzpicture}

Taita kulmittain (2 kpl).

\begin{tikzpicture}
\input{reverseclip.tex}
\input{coordinates.tex}
\def\orientation{1}
\input{orientation.tex}

\filldraw[\pfront] (a) -- (b) -- (c) -- (d) -- cycle;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%ready lines
\draw[\stylea] (n)--(s);
\draw[\stylea] (w)--(e);
\draw[\stylea] (na)--(sb);
\draw[\stylea] (nd)--(sc);
\draw[\stylea] (wc)--(eb);
\draw[\stylea] (wd)--(ea);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\filldraw[\ptable] (a)--(b)--(c)--cycle;
\filldraw[\pback] (c)--(d)--(a)--cycle;
\draw (a) -- (c);
\foldpoint{b}{d}{right}
\draw[black,thin] (a)--(b)--(c)--(d)--cycle;
\end{tikzpicture}
\begin{tikzpicture}
\input{reverseclip.tex}
\input{coordinates.tex}
\def\orientation{1}
\input{orientation.tex}

\filldraw[\pfront] (a) -- (b) -- (c) -- (d) -- cycle;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%ready lines
\draw[\stylea] (n)--(s);
\draw[\stylea] (w)--(e);
\draw[\stylea] (na)--(sb);
\draw[\stylea] (nd)--(sc);
\draw[\stylea] (wc)--(eb);
\draw[\stylea] (wd)--(ea);
\draw[\styleb] (ea)--(sc);
\draw[\styleb] (sb)--(wd);
\draw[\styleb] (wc)--(na);
\draw[\styleb] (nd)--(eb);
\draw[\stylea] (a)--(c);
\draw[dotted] (b)--(d);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\draw[black,thin] (a)--(b)--(c)--(d)--cycle;
\end{tikzpicture}

Loppu on hieman hankala. Katso video [5:11$\to$]:\\
\url{https://www.youtube.com/watch?v=7vXVblyJnqY&t=311}

\end{document}