$x=2\left(\sqrt{5}\cos(\frac{\arccos(\frac{4\sqrt{5}}{25})}{3})+2\right)\approx 8.116250286\text{, }y=40\sqrt{5}\left(\cos(\frac{\arccos(\frac{4\sqrt{5}}{25})}{3})\right)^{3}-18\sqrt{5}\cos(\frac{\arccos(\frac{4\sqrt{5}}{25})}{3})+60\left(\cos(\frac{\arccos(\frac{4\sqrt{5}}{25})}{3})\right)^{2}-17\approx 66.528050961\text{, }z=4$
$x=-\sqrt{5}\left(\sqrt{3}\sin(\frac{\arccos(\frac{4\sqrt{5}}{25})}{3})+\cos(\frac{\arccos(\frac{4\sqrt{5}}{25})}{3})\right)+4\approx 0.427819809\text{, }y=\left(-\sqrt{5}\left(\sqrt{3}\sin(\frac{\arccos(\frac{4\sqrt{5}}{25})}{3})+\cos(\frac{\arccos(\frac{4\sqrt{5}}{25})}{3})\right)+4\right)^{3}-9\left(-\sqrt{5}\left(\sqrt{3}\sin(\frac{\arccos(\frac{4\sqrt{5}}{25})}{3})+\cos(\frac{\arccos(\frac{4\sqrt{5}}{25})}{3})\right)+4\right)^{2}-15\sqrt{5}\left(\sqrt{3}\sin(\frac{\arccos(\frac{4\sqrt{5}}{25})}{3})+\cos(\frac{\arccos(\frac{4\sqrt{5}}{25})}{3})\right)+63\approx 7.848332804\text{, }z=4$
$x=\sqrt{5}\left(\sqrt{3}\sin(\frac{\arccos(\frac{4\sqrt{5}}{25})}{3})-\cos(\frac{\arccos(\frac{4\sqrt{5}}{25})}{3})\right)+4\approx 3.455929905\text{, }y=\left(\sqrt{5}\left(\sqrt{3}\sin(\frac{\arccos(\frac{4\sqrt{5}}{25})}{3})-\cos(\frac{\arccos(\frac{4\sqrt{5}}{25})}{3})\right)+4\right)^{3}-9\left(\sqrt{5}\left(\sqrt{3}\sin(\frac{\arccos(\frac{4\sqrt{5}}{25})}{3})-\cos(\frac{\arccos(\frac{4\sqrt{5}}{25})}{3})\right)+4\right)^{2}+15\sqrt{5}\left(\sqrt{3}\sin(\frac{\arccos(\frac{4\sqrt{5}}{25})}{3})-\cos(\frac{\arccos(\frac{4\sqrt{5}}{25})}{3})\right)+63\approx -11.376383765\text{, }z=4$