Image:V-E+F=2 Proof Illustration.svg

Summary

Generated from the following MetaPost code:

beginfig(1)
  pair A[], B[], C[];
  A[0]:=(1cm, 1cm); A[1]:=(5cm, 1cm);
  A[2]:=(5cm, 5cm); A[3]:=(1cm, 5cm);
  A[4]:=(2cm, 2cm); A[5]:=(4cm, 2cm);
  A[6]:=(4cm, 4cm); A[7]:=(2cm, 4cm);
  for i = 0 upto 7:
    draw A[i] withpen pencircle scaled 6pt;
    B[i] = A[i] + (6cm, 0cm);
    draw B[i] withpen pencircle scaled 6pt;
    C[i] = A[i] + (12cm, 0cm);
    draw C[i] withpen pencircle scaled 6pt;
  endfor;
  draw A[0]--A[1]--A[2]--A[3]--cycle;
  draw A[4]--A[5]--A[6]--A[7]--cycle;
  draw A[0]--A[4]; draw A[1]--A[5];
  draw A[2]--A[6]; draw A[3]--A[7];
  draw B[0]--B[1] dashed evenly;
  draw B[1]--B[2]--B[3]--B[0];
  draw B[4]--B[5]--B[6]--B[7]--cycle;
  draw B[0]--B[4];
  draw B[1]--B[5]; draw B[2]--B[6];
  draw B[3]--B[7]; draw B[4]--B[6];
  draw B[0]--B[5];
  draw B[1]--B[6]; draw B[2]--B[7];
  draw B[3]--B[4];
  draw C[1]--C[2]--C[3];
  draw C[4]--C[5]--C[6]--C[7]--cycle;
  draw C[0]--C[4] dashed evenly;
  draw C[1]--C[5]; draw C[2]--C[6];
  draw C[3]--C[7]; draw C[4]--C[6];
  draw C[0]--C[5] dashed evenly;
  draw C[1]--C[6]; draw C[2]--C[7];
  draw C[3]--C[4];
endfig;
end;

Licensing

I, the copyright holder of this work, hereby release it into the public domain. This applies worldwide. In case this is not legally possible: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. Afrikaans | Alemannisch | Aragonés | العربية | Asturianu | Български | Català | Cebuano | Česky | Cymraeg | Dansk | Deutsch | Eʋegbe | Ελληνικά | English | Español | Esperanto | Euskara | Estremeñu | فارسی | Français | Galego | 한국어 | हिन्दी | Hrvatski | Ido | Bahasa Indonesia | Íslenska | Italiano | עברית | Kurdî / كوردی | Latina | Lietuvių | Latviešu | Magyar | Македонски | Bahasa Melayu | Nederlands | ‪Norsk (bokmål)‬ | ‪Norsk (nynorsk)‬ | 日本語 | Polski | Português | Ripoarisch | Română | Русский | Shqip | Slovenčina | Slovenščina | Српски / Srpski | Suomi | Svenska | ไทย | Tagalog | Türkçe | Українська | Tiếng Việt | Walon | ‪中文(简体)‬ | ‪中文(繁體)‬ | zh-yue-hant | +/-