I'm reading a paper that has the following statement: The equation $m = n^2 - p_1^2 - p_2^2 - p_3^2$ expresses the area measured in triangles, as a quadratic form of signature $(1, 3)$. The isometry group of any such form is $\mathbb{Z}_2 \times \operatorname{Isom}(\mathbb{H}^3)$ (here $\mathbb{Z}_2$ is the cyclic group of order $2$.)
I understand the first part of the statement. Could someone explain or point me to a reference about the second statement about Isometries of such a form?