Z4

Z4
(3D model) (OFF file)
Rank	3
Space	Spherical
Notation
Stewart notation	Z4
Elements
Faces	2 squares, 2+2+4+4+4+4 triangles
Edges	2+2+2+4+4+4+4+4+4+4
Vertices	2+2+2+4+4
Measures (edge length 1)
Height	$\frac{1+\sqrt{5}}{2}\approx 1.61803$
Central density	1
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Genus	0
Properties
Symmetry	K2+×A1, order 4
Convex	No

Z₄ is a non-convex regular faced polyhedron. Although it is spherical, it is used for tunneling many Stewart toroids.

Vertex coordinates

The vertex coordinates for Z₄ with unit side length are:

• $\left(\pm\frac12,\pm\frac12,\pm\frac{1+\sqrt{5}}4\right)$,
• $\left(\pm\frac{1+\sqrt{5}}4,0,0\right)$,
• $\pm\left(0,\frac{5+3\sqrt{5}}{20},\frac{2\sqrt{5}-5}{10}\right)$,
• $\pm\left(0,\frac{\sqrt{5}-1}{4},\frac12\right)$.