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You may look into what is called $\Delta$-complexes, and may be the notion of a $\Delta$-complex will suit you. There you give an orientation to each simplex and then glue them by using face maps, whi …

Here's a question that (I hope) may seem very trivial for you, and I hope one of you may provide me with a reference answering it (unless it's a trivial colloquial knowledge). Let $f$ be an indefini …

The identities $L_2(\frac{\sqrt{5}-1}{2}) = \frac{\pi^2}{10}$ and $L_2(\frac{3-\sqrt{5}}{2}) = \frac{\pi^2}{15}$ are due to J. Landen. The rest of the identities you wrote, I suppose, could be obtaine …

Motivation: This question is related to my study of hyperbolic Coxeter polytopes. In general, if one put some restrictions on the type of their dihedral angles (say, all dihedral angles are equal to $ …

Dear Colleagues and Friends, Here I need to find some good reference on a subject that seems very much studied: sorry, if the rest of this question is too naive. I believe that it's known that if a co …

The group itself shall be the group generated by reflections in the sides of a regular ideal tetrahedron, whose dihedral angles are all $\pi/3$. For a reference, there are many Coxeter diagrams liste …