Z4

Z4
(3D model) (OFF file)
Rank	3
Notation
Stewart notation	Z4
Elements
Faces	2 squares, 2+2+4×4 triangles
Edges	3×2+7×4
Vertices	2+2+2+4+4
Measures (edge length 1)
Volume	${\frac {7+3{\sqrt {5}}}{12}}\approx 1.14235$
Height	${\frac {1+{\sqrt {5}}}{2}}\approx 1.61803$
Central density	1
Abstract & topological properties
Flag count	136
Euler characteristic	2
Orientable	Yes
Genus	0
Properties
Symmetry	K2+×A1, order 4
Flag orbits	34
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:

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