Is there a volume formula for hyperbolic truncated tetrahedron? Which seems looks like Yu. Cho and H. Kim, Discrete Comput. Geom. 22, 347–366 (1999).



1 Answer 1


Look for the volume of a simplex. Suppose you have $n+1$ affine independent column vectors $v_1,v_2,\cdots,v_{n+1}$ in $\mathbb R^n$ then the simplex of these points(convex hull of them) has volume:

$$\det \begin{bmatrix} 1 & 1 & \cdots & 1 \\ v_1 & v_2 & \cdots & v_{n+1} \\ \end{bmatrix} $$

Now you can split hyperbolic truncated tetrahedron to some simplex.

  • $\begingroup$ Thanks. But I mean the formula which only contains the “geometrical product”(such as Angle, length)... $\endgroup$
    – user117580
    Commented Jan 20, 2018 at 14:58
  • $\begingroup$ @user117580 Really I don't know. But I guess there should be some thing like that you want. $\endgroup$
    – GhD
    Commented Jan 20, 2018 at 15:05

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