Triaugmented Triangular Prism

$\begin{figure}\BoxedEPSF{J51_net.epsf scaled 500}\end{figure}$

One of the convex Deltahedra and Johnson Solid $J_{51}$ . The Vertices are $(\pm 1, \pm 1, 0)$ , $(0, 0, \sqrt{2}\,)$ , $(0, \pm 1, -\sqrt{3}\,)$ , $(\pm (1+\sqrt{6}\,)/2, 0, -(\sqrt{2}+\sqrt{3}\,)/2)$ , where the and coordinates of the last are found by solving

$\displaystyle x^2+1^2+(z+\sqrt{3}\,)^2$	$\textstyle =$	$\displaystyle 2^2$
$\displaystyle (x-1)^2+1^2+z^2$	$\textstyle =$	$\displaystyle 2^2.$

See also Deltahedron, Johnson Solid