From b879ffd58aa2c74b8f7b199edfa4b108b88c6e0b Mon Sep 17 00:00:00 2001
From: Nao Pross <np@0hm.ch>
Date: Fri, 7 May 2021 00:12:11 +0200
Subject: Create slide to show all point groups

---
 vorlesungen/punktgruppen/slides.tex | 265 +++++++++++++++++++++++++++++++++++-
 1 file changed, 263 insertions(+), 2 deletions(-)

(limited to 'vorlesungen/punktgruppen/slides.tex')

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
-- 
cgit v1.2.1

