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-rw-r--r--vorlesungen/punktgruppen/.gitignore1
-rw-r--r--vorlesungen/punktgruppen/Makefile3
-rw-r--r--vorlesungen/punktgruppen/slides.pdfbin871227 -> 789335 bytes
-rw-r--r--vorlesungen/punktgruppen/slides.tex265
4 files changed, 265 insertions, 4 deletions
diff --git a/vorlesungen/punktgruppen/.gitignore b/vorlesungen/punktgruppen/.gitignore
index 3d67444..841ea7e 100644
--- a/vorlesungen/punktgruppen/.gitignore
+++ b/vorlesungen/punktgruppen/.gitignore
@@ -8,4 +8,5 @@ build
# files
script.log
slides.log
+slides.vrb
missfont.log
diff --git a/vorlesungen/punktgruppen/Makefile b/vorlesungen/punktgruppen/Makefile
index d685652..302e976 100644
--- a/vorlesungen/punktgruppen/Makefile
+++ b/vorlesungen/punktgruppen/Makefile
@@ -1,12 +1,11 @@
TEX=xelatex
-TEXARGS=--output-directory=build --halt-on-error
+TEXARGS=--output-directory=build --halt-on-error --shell-escape
all: slides.pdf script.pdf media
.PHONY: clean
clean:
@rm -rfv build
- # @rm -rfv media
%.pdf: %.tex
mkdir -p build
diff --git a/vorlesungen/punktgruppen/slides.pdf b/vorlesungen/punktgruppen/slides.pdf
index 715d915..78cd5dd 100644
--- a/vorlesungen/punktgruppen/slides.pdf
+++ b/vorlesungen/punktgruppen/slides.pdf
Binary files differ
diff --git a/vorlesungen/punktgruppen/slides.tex b/vorlesungen/punktgruppen/slides.tex
index da13003..08b6ecb 100644
--- a/vorlesungen/punktgruppen/slides.tex
+++ b/vorlesungen/punktgruppen/slides.tex
@@ -1,4 +1,4 @@
-\documentclass[12pt, xcolor, aspectratio=169]{beamer}
+\documentclass[12pt, xcolor, aspectratio=169, handout]{beamer}
% language
\usepackage{polyglossia}
@@ -8,8 +8,16 @@
\usepackage{tikz}
\usetikzlibrary{positioning}
\usetikzlibrary{arrows.meta}
+\usetikzlibrary{shapes.misc}
\usetikzlibrary{calc}
+\usetikzlibrary{external}
+\tikzexternalize[
+ mode = graphics if exists,
+ figure list = true,
+ prefix=build/
+]
+
% Theme
\beamertemplatenavigationsymbolsempty
@@ -399,13 +407,266 @@
Somit muss
\begin{align*}
\alpha &= \cos^{-1}\left(\frac{1-n}{2}\right) \\[1em]
- \alpha &\in \left\{ 0, 60^\circ, 90^\circ, 120^\circ, 180^\circ \right\}
+ \alpha &\in \left\{ 0, 60^\circ, 90^\circ, 120^\circ, 180^\circ \right\} \\
+ n &\in \left\{ 1, 2, 3, 4, 6 \right\}
\end{align*}
}
\end{column}
\end{columns}
\end{frame}
+{
+ \usebackgroundtemplate[fragile]{
+ \begin{tikzpicture}[
+ overlay,
+ xshift = .45\paperwidth,
+ yshift = .47\paperheight,
+ classcirc/.style = {
+ draw = gray, thick, circle,
+ minimum size = 12mm,
+ inner sep = 0pt, outer sep = 0pt,
+ },
+ classlabel/.style = {
+ below right = 5mm
+ },
+ round/.style = {
+ draw = yellow, thick, circle,
+ minimum size = 1mm,
+ inner sep = 0pt, outer sep = 0pt,
+ },
+ cross/.style = {
+ cross out, draw = magenta, thick,
+ minimum size = 1mm,
+ inner sep = 0pt, outer sep = 0pt
+ },
+ ]
+ \matrix [row sep = 3mm, column sep = 0mm] {
+ \node[classcirc] (C1) {} node[classlabel] {\(C_{1}\)}; &
+ \node[classcirc] (C2) {} node[classlabel] {\(C_{2}\)}; &
+ \node[classcirc] (C3) {} node[classlabel] {\(C_{3}\)}; &
+ \node[classcirc] (Ci) {} node[classlabel] {\(C_{i}\)}; &
+
+ \node[classcirc] (Cs) {} node[classlabel] {\(C_{s}\)}; &
+ \node[classcirc] (C3i) {} node[classlabel] {\(C_{3i}\)}; &
+ \node[classcirc] (C2h) {} node[classlabel] {\(C_{2h}\)}; &
+ \node[classcirc] (D2) {} node[classlabel] {\(D_{2}\)}; \\
+
+ \node[classcirc] (D3d) {} node[classlabel] {\(D_{3d}\)}; &
+ \node[classcirc] (C2v) {} node[classlabel] {\(C_{2v}\)}; &
+ \node[classcirc] (D2h) {} node[classlabel] {\(D_{2h}\)}; &
+ \node[classcirc] (D3) {} node[classlabel] {\(D_{3}\)}; &
+
+ \node[classcirc] (C4) {} node[classlabel] {\(C_{4}\)}; &
+ \node[classcirc] (C6) {} node[classlabel] {\(C_{6}\)}; &
+ \node[classcirc] (D3dP) {} node[classlabel] {\(D_{3d}\)}; &
+ \node[classcirc] (S4) {} node[classlabel] {\(S_{4}\)}; \\
+
+ \node[classcirc] (S3) {} node[classlabel] {\(S_{3}\)}; &
+ \node[classcirc, dashed] (T) {} node[classlabel] {\(T_{}\)}; &
+ \node[classcirc] (C4h) {} node[classlabel] {\(C_{4h}\)}; &
+ \node[classcirc] (C6h) {} node[classlabel] {\(C_{6h}\)}; &
+
+ \node[classcirc, dashed] (Th) {} node[classlabel] {\(T_{h}\)}; &
+ \node[classcirc] (C4v) {} node[classlabel] {\(C_{4v}\)}; &
+ \node[classcirc] (C6v) {} node[classlabel] {\(C_{6v}\)}; &
+ \node[classcirc, dashed] (Td) {} node[classlabel] {\(T_{d}\)}; \\
+
+ \node[classcirc] (D2d) {} node[classlabel] {\(D_{2d}\)}; &
+ \node[classcirc] (D3h) {} node[classlabel] {\(D_{3h}\)}; &
+ \node[classcirc, dashed] (O) {} node[classlabel] {\(O_{}\)}; &
+ \node[classcirc] (D4) {} node[classlabel] {\(D_{4}\)}; &
+
+ \node[classcirc] (D6) {} node[classlabel] {\(D_{6}\)}; &
+ \node[classcirc, dashed] (Oh) {} node[classlabel] {\(O_{h}\)}; &
+ \node[classcirc] (D4h) {} node[classlabel] {\(D_{4h}\)}; &
+ \node[classcirc] (D6h) {} node[classlabel] {\(D_{6h}\)}; \\
+ };
+
+
+ \node[cross] at ($(C1)+(4mm,0)$) {};
+
+
+ \node[cross] at ($(C2)+(4mm,0)$) {};
+ \node[cross] at ($(C2)-(4mm,0)$) {};
+
+
+ \node[cross] at ($(C3)+( 0:4mm)$) {};
+ \node[cross] at ($(C3)+(120:4mm)$) {};
+ \node[cross] at ($(C3)+(240:4mm)$) {};
+
+
+ \node[cross] at ($(Ci)+(4mm,0)$) {};
+ \node[round] at ($(Ci)-(4mm,0)$) {};
+
+
+ \node[cross] at ($(Cs)+(4mm,0)$) {};
+ \node[round] at ($(Cs)+(4mm,0)$) {};
+
+
+ \node[cross] at ($(C3i)+( 0:4mm)$) {};
+ \node[cross] at ($(C3i)+(120:4mm)$) {};
+ \node[cross] at ($(C3i)+(240:4mm)$) {};
+ \node[round] at ($(C3i)+( 60:4mm)$) {};
+ \node[round] at ($(C3i)+(180:4mm)$) {};
+ \node[round] at ($(C3i)+(300:4mm)$) {};
+
+
+ \node[cross] at ($(C2h)+(4mm,0)$) {};
+ \node[cross] at ($(C2h)-(4mm,0)$) {};
+ \node[round] at ($(C2h)+(4mm,0)$) {};
+ \node[round] at ($(C2h)-(4mm,0)$) {};
+
+
+ \node[cross] at ($(D2)+( 20:4mm)$) {};
+ \node[cross] at ($(D2)+(200:4mm)$) {};
+ \node[round] at ($(D2)+(160:4mm)$) {};
+ \node[round] at ($(D2)+(340:4mm)$) {};
+
+
+ \foreach \x in {0, 120, 240} {
+ \node[cross] at ($(D3d)+({\x+15}:4mm)$) {};
+ \node[cross] at ($(D3d)+({\x-15}:4mm)$) {};
+ }
+
+
+ \foreach \x in {0, 180} {
+ \node[cross] at ($(C2v)+({\x+15}:4mm)$) {};
+ \node[cross] at ($(C2v)+({\x-15}:4mm)$) {};
+ }
+
+
+ \foreach \x in {0, 180} {
+ \node[cross] at ($(D2h)+({\x+15}:4mm)$) {};
+ \node[cross] at ($(D2h)+({\x-15}:4mm)$) {};
+ \node[round] at ($(D2h)+({\x+15}:4mm)$) {};
+ \node[round] at ($(D2h)+({\x-15}:4mm)$) {};
+ }
+
+
+ \foreach \x in {0, 120, 240} {
+ \node[cross] at ($(D3)+({\x+15}:4mm)$) {};
+ \node[round] at ($(D3)+({\x-15}:4mm)$) {};
+ }
+
+
+ \foreach \x in {0, 90, 180, 270} {
+ \node[cross] at ($(C4)+(\x:4mm)$) {};
+ }
+
+
+ \foreach \x in {0, 60, 120, 180, 240, 300} {
+ \node[cross] at ($(C6)+(\x:4mm)$) {};
+ }
+
+
+ \foreach \x in {0, 120, 240} {
+ \node[cross] at ($(D3dP)+({\x+15}:4mm)$) {};
+ \node[cross] at ($(D3dP)+({\x-15}:4mm)$) {};
+ \node[round] at ($(D3dP)+({\x+15+60}:4mm)$) {};
+ \node[round] at ($(D3dP)+({\x-15+60}:4mm)$) {};
+ }
+
+
+ \node[cross] at ($(S4)+(4mm,0)$) {};
+ \node[cross] at ($(S4)-(4mm,0)$) {};
+ \node[round] at ($(S4)+(0,4mm)$) {};
+ \node[round] at ($(S4)-(0,4mm)$) {};
+
+
+ \foreach \x in {0, 120, 240} {
+ \node[cross] at ($(S3)+(\x:4mm)$) {};
+ \node[round] at ($(S3)+(\x:4mm)$) {};
+ }
+
+
+ %% TODO: T
+
+
+ \foreach \x in {0, 90, 180, 270} {
+ \node[cross] at ($(C4h)+(\x:4mm)$) {};
+ \node[round] at ($(C4h)+(\x:4mm)$) {};
+ }
+
+
+ \foreach \x in {0, 60, 120, 180, 240, 300} {
+ \node[cross] at ($(C6h)+(\x:4mm)$) {};
+ \node[round] at ($(C6h)+(\x:4mm)$) {};
+ }
+
+
+ %% TODO: Th
+
+
+ \foreach \x in {0, 90, 180, 270} {
+ \node[cross] at ($(C4v)+(\x+15:4mm)$) {};
+ \node[cross] at ($(C4v)+(\x-15:4mm)$) {};
+ }
+
+
+
+ \foreach \x in {0, 60, 120, 180, 240, 300} {
+ \node[cross] at ($(C6v)+(\x+10:4mm)$) {};
+ \node[cross] at ($(C6v)+(\x-10:4mm)$) {};
+ }
+
+
+ %% TODO: Td
+
+
+ \foreach \x in {0, 180} {
+ \node[cross] at ($(D2d)+({\x+15}:4mm)$) {};
+ \node[round] at ($(D2d)+({\x-15}:4mm)$) {};
+
+ \node[round] at ($(D2d)+({\x+15+90}:4mm)$) {};
+ \node[cross] at ($(D2d)+({\x-15+90}:4mm)$) {};
+ }
+
+
+ \foreach \x in {0, 120, 240} {
+ \node[cross] at ($(D3h)+({\x+15}:4mm)$) {};
+ \node[cross] at ($(D3h)+({\x-15}:4mm)$) {};
+ \node[round] at ($(D3h)+({\x+15}:4mm)$) {};
+ \node[round] at ($(D3h)+({\x-15}:4mm)$) {};
+ }
+
+
+ %% TODO: O
+
+
+ \foreach \x in {0, 90, 180, 270} {
+ \node[cross] at ($(D4)+({\x+15}:4mm)$) {};
+ \node[round] at ($(D4)+({\x-15}:4mm)$) {};
+ }
+
+ \foreach \x in {0, 60, 120, 180, 240, 300} {
+ \node[cross] at ($(D6)+({\x+10}:4mm)$) {};
+ \node[round] at ($(D6)+({\x-10}:4mm)$) {};
+ }
+
+
+ % TODO Oh
+
+
+ \foreach \x in {0, 90, 180, 270} {
+ \node[cross] at ($(D4h)+(\x+15:4mm)$) {};
+ \node[cross] at ($(D4h)+(\x-15:4mm)$) {};
+ \node[round] at ($(D4h)+(\x+15:4mm)$) {};
+ \node[round] at ($(D4h)+(\x-15:4mm)$) {};
+ }
+
+
+ \foreach \x in {0, 60, 120, 180, 240, 300} {
+ \node[cross] at ($(D6h)+({\x+10}:4mm)$) {};
+ \node[cross] at ($(D6h)+({\x-10}:4mm)$) {};
+ \node[round] at ($(D6h)+({\x+10}:4mm)$) {};
+ \node[round] at ($(D6h)+({\x-10}:4mm)$) {};
+ }
+ \end{tikzpicture}
+ }
+ \begin{frame}[fragile]{}
+ \end{frame}
+}
+
\section{Anwendungen}
\begin{frame}[fragile]{}
\centering