User:Hyacinth67/sandbox

 The following define the vertices of a bilunabirotunda centered at the origin with edge length 1:  $$(0, 0, \pm\frac{1+\sqrt{2-\varphi}}{2}$$) $$(\pm\frac{\sqrt{5\varphi-2\sqrt{2-\varphi}}}{2}, \pm\frac{1}{2}, 0)$$ $$(\pm\frac{1}{2},\pm\frac{\varphi}{2},\pm\frac{1}{2})$$  where $$\varphi=\frac{1+\sqrt{5}}{2} $$ is the golden ratio.