number | name | Description | Example |

0 | Isolated tetrahedron | T | |

1 | v10 | one vertex | V_{1} |

2 | v21 | two vertices | V_{1}, V_{2} |

3 | v33 | three vertices | V_{1}, V_{2}, V_{3} |

4 | v46 | four vertices | V_{1}, V_{2}, V_{3}, V_{4} |

5 | e10 | one edge | E_{12} |

6 | e20 | two opposite edges | E_{12}, E_{34} |

7 | e21 | two edges sharing a vertex | E_{12}, E_{23} |

8 | e32 | three edges forming a path | E_{12}, E_{23}, E_{34} |

9 | e33 | three edges sharing a vertex | E_{12}, E_{13}, E_{14} |

10 | e33F | three edges on one face | E_{12}, E_{23}, E_{31} |

11 | e44 | four edges forming a loop | E_{12}, E_{23}, E_{34}, E_{41} |

12 | e45 | four edges not forming a loop | E_{12}, E_{23}, E_{31}, E_{14} |

13 | e56 | five edges | E_{12}, E_{13}, E_{14}, E_{23}, E_{24} |

14 | e612 | six edges | E_{12}, E_{13}, E_{14}, E_{23}, E_{24}, E_{34} |

15 | ev11 | one edge and one vertex | E_{12}, V_{3} |

16 | ev12 | one edge and two vertices | E_{12}, V_{3}, V_{4} |

17 | ev21 | two edges and one vertex | E_{12}, E_{23}, V_{4} |

18 | ev31 | three edges and one vertex | E_{12}, E_{23}, E_{31}, V_{4} |

19 | fe11 | one face and one edge | F_{123}, E_{14} |

20 | fe12 | one face and two edges | F_{123}, E_{14}, E_{24} |

21 | fe13 | one face and three edges | F_{123}, E_{14}, E_{24}, E_{34} |

22 | fe21 | two faces and one edge | F_{123}, F_{124}, E_{34} |

23 | f1 | one face | F_{123} |

24 | f2 | two faces | F_{123}, F_{124} |

25 | f3 | three faces | F_{123}, F_{124}, F_{134} |

26 | f4 | four faces | F_{123}, F_{124}, F_{134}, F_{234} |

27 | fv | one face and the opposite vertex | F_{123}, V_{4} |

The example illustrates the facets on which a tetrahedron with vertices 1 through 4 is joined. Both the reference number and the name of each step are used internally in the software.