- The { Tetrahedron } is core and central to the { Four Body Problem } ,
- and 6 Degrees-Of-Freedom ( DOF's ) are usually involved in defining the { size and shape } of the { Tetrahedron } .

- We noticed that the { line } joining the mid-points on each pair of { non-touching / opposite sides } always passes thru the { centroid } of the { Tetrahedron } ,
- and this set of { 3 lines } may then be used to fully define the 6-sided { Tetrahedron } .

- The method of construction is as follows :
- Take 3 sticks of any arbitrary lengths and orient these in { 3-D space } so that :
- the 3 sticks bisect one-another .

The { point-of-intersection } for the { 3 sticks } is then the { centroid } of the { Tetrahedron } , and :

- the 6 end-points on the { 3-sticks } then match exactly onto the 6 mid-points on the { 6 sides } .

This then fully defines { Tetrahedron } .

- Take 3 sticks of any arbitrary lengths and orient these in { 3-D space } so that :
- Hopefully , this will lead to a better understanding of the { Four Body Problem } , and further .

Links to other Sections | |
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Section I | Setting up the Reference Frames |

Section II | The 12 Degrees-Of-Freedom for the Tetrahedron |

Section III | The 5 Categories of Tetrahedra |

Section IV | Constructing the { General Tetrahedron } |

Section V | The { Flattened Tetrahedron } |

Section VI | Brief Summary on the Tetrahedron |

Section VII | Setting up for Angular Momentum Issues |

Section VIII | Cross-Product Considerations |

Section IX | Concluding Remarks |

Appendix A | A Numerical Example for the Cross-Product of 2 Tetrahedra |

Epilogs added 2008-1-07 | |
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Epilog I | An Elaboration on the Cross-Product [ T-on-T ] |

Epilog II | On the { [ Zero ] Angular Momentum Vector } |

Epilog III | On { Mirror / Rotated / Counter Images } |

( Three Body Problem / Characteristics of Numbers / Matrix & Linear Algebra / 'I-CHING' / Triangle / Odd-On-Odd Format / Multiplication Table for Modulo P / Symmetry and Combinatorics / Solid Object with 14 Faces )