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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 $x$ and $z$ 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

© 1996-9 Eric W. Weisstein