Merge remote-tracking branch 'upstream/master'

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diff --git a/buch/chapters/95-homologie/images/polyeder.tex b/buch/chapters/95-homologie/images/polyeder.tex
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+++ b/buch/chapters/95-homologie/images/polyeder.tex
@@ -0,0 +1,109 @@
+%
+% tikztemplate.tex -- template for standalon tikz images
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+\usepackage{pgfplots}
+\usepackage{csvsimple}
+\usetikzlibrary{arrows,intersections,math,calc}
+\begin{document}
+\def\skala{1}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+% add image content here
+\begin{scope}[xshift=-3.5cm,scale=0.5]
+\coordinate (A) at (0,0);
+\coordinate (B) at (4,0);
+\coordinate (C) at (5,-2);
+\coordinate (D) at (8,-1);
+\coordinate (E) at (7,1);
+\coordinate (F) at (7,3);
+\coordinate (G) at (1,3);
+\coordinate (H) at (5,4);
+\coordinate (I) at (9,5);
+\coordinate (J) at (4,7);
+\coordinate (K) at (-1,9);
+\coordinate (L) at (7,11);
+\coordinate (M) at (6,-0.5);
+
+\fill[color=gray,opacity=0.5] (A)--(B)--(H)--(G)--cycle;
+\fill[color=gray,opacity=0.5] (G)--(I)--(K)--cycle;
+\fill[color=gray,opacity=0.5] (G)--(L)--(K)--cycle;
+
+\draw (K)--(G)--(A)--(B)--(D);
+\draw (C)--(E);
+\draw (G)--(I)--(K);
+\draw (G)--(L)--(K);
+\draw (B)--(H);
+\draw (B)--(F);
+
+\fill (A) circle[radius=0.1];
+\fill (B) circle[radius=0.1];
+\fill (C) circle[radius=0.1];
+\fill (D) circle[radius=0.1];
+\fill (E) circle[radius=0.1];
+\fill (F) circle[radius=0.1];
+\fill (G) circle[radius=0.1];
+\fill (H) circle[radius=0.1];
+\fill (I) circle[radius=0.1];
+%\fill (J) circle[radius=0.1];
+\fill (K) circle[radius=0.1];
+\fill (L) circle[radius=0.1];
+%\fill (M) circle[radius=0.1];
+
+\draw[color=red] (H) circle[radius=0.5];
+\draw[color=red] (J) circle[radius=0.5];
+\draw[color=red] (M) circle[radius=0.5];
+\draw[color=red] ($0.25*(A)+0.25*(B)+0.25*(G)+0.25*(H)$) circle[radius=0.5];
+
+\end{scope}
+
+\begin{scope}[xshift=3.5cm,scale=0.5]
+\coordinate (A) at (0,0);
+\coordinate (B) at (4,0);
+\coordinate (C) at (5,-2);
+\coordinate (D) at (8,-1);
+\coordinate (E) at (7,1);
+\coordinate (F) at (7,3);
+\coordinate (G) at (1,3);
+\coordinate (H) at (5,4);
+\coordinate (I) at (9,5);
+\coordinate (J) at (4,7);
+\coordinate (K) at (-1,9);
+\coordinate (L) at (7,11);
+\coordinate (M) at (6,-0.5);
+
+\fill[color=gray!50] (A)--(B)--(H)--(I)--(J)--(L)--(K)--(G)--cycle;
+
+\draw (K)--(G)--(A)--(B)--(D);
+\draw (C)--(E);
+\draw (G)--(I)--(K);
+\draw (G)--(L)--(K);
+\draw (B)--(H);
+\draw (B)--(F);
+\draw (H)--(J);
+\draw (A)--(H);
+
+\fill (A) circle[radius=0.1];
+\fill (B) circle[radius=0.1];
+\fill (C) circle[radius=0.1];
+\fill (D) circle[radius=0.1];
+\fill (E) circle[radius=0.1];
+\fill (F) circle[radius=0.1];
+\fill (G) circle[radius=0.1];
+\fill (H) circle[radius=0.1];
+\fill (I) circle[radius=0.1];
+\fill (J) circle[radius=0.1];
+\fill (K) circle[radius=0.1];
+\fill (L) circle[radius=0.1];
+\fill (M) circle[radius=0.1];
+
+\end{scope}
+
+\end{tikzpicture}
+\end{document}
+