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.

中文翻译：

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费曼积分的三角图、距离几何和对称性

我们通过费曼积分的对称性 (SFI) 方法研究最一般的三角图。在简单的基础上获得并呈现了 SFI 方程组。该系统解决了提供基本已知表达的新推导。我们强调根据 Davydychev-Delbourgo [1] 讨论的四面体的距离几何来描述底层几何，这是一个四面体，它是双壳图。此外，还识别了奇异轨迹，并将图在轨迹两个分量上的值表示为后代气泡图的线性组合。重新审视无质量三角形和相关的魔法连接。