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Informally, right-angled hyperbolic hexagon is a hyperbolic triangle with vertices outside infinity. I think there should be a Gram matrix for it, and what does it looks like? (The Gram matrix here defines the existence of a simplex)

Also, for hyperbolic truncated tetrahedron or hyperbolic truncated n-simplex what’s the form of its Gram matrix?

Thanks.

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  • $\begingroup$ What is the definition of Gram matrix in this context? $\endgroup$
    – j.c.
    Commented Dec 11, 2017 at 16:33
  • $\begingroup$ @j.c. It defines the existence of a simplex. Thanks. $\endgroup$
    – user117580
    Commented Dec 11, 2017 at 16:35

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Why do you mean by "what is the form"? And which Gram matrix? (there are two). But if you mean the usual Gram matrix, then the $ij$ element is $-\cosh d(s_i, s_j),$ where $s_i$ is the $2i$-th side of the hexagon.

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