## Abstract

We study the most general triangle diagram through the Symmetries of Feynman Integrals (SFI) approach. The SFI equation system is obtained and presented in a simple basis. The system is solved providing a novel derivation of an essentially known expression. We stress a description of the underlying geometry in terms of the Distance Geometry of a tetrahedron discussed by Davydychev-Delbourgo [1], a tetrahedron which is the dual on-shell diagram. In addition, the singular locus is identified and the diagram’s value on the locus’s two components is expressed as a linear combination of descendant bubble diagrams. The massless triangle and the associated magic connection are revisited.

Original language | American English |
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Article number | 156 |

Journal | Journal of High Energy Physics |

Volume | 2020 |

Issue number | 3 |

DOIs | |

State | Published - 1 Mar 2020 |

### Bibliographical note

Funding Information:This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited

Publisher Copyright:

© 2020, The Author(s).

## Keywords

- Differential and Algebraic Geometry
- Scattering Amplitudes