Bilinski dodecahedron

Bilinski dodecahedron
(3D model) (OFF file)
Rank	3
Elements
Faces	8 + 2 + 2 golden rhombi
Edges	4 + 4 + 4 + 8
Vertices	2 + 4 + 4 + 4
Measures (edge length 1)
Central density	1
Abstract & topological properties
Flag count	96
Euler characteristic	2
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	K3, order 8
Convex	Yes
Nature	Tame

The Bilinski dodecahedron is a polyhedron with twelve golden rhombus faces. It is topologically equivalent to the rhombic dodecahedron. It is one of the five golden isozonohedra.

Vertex coordinates

The vertex coordinates of a Bilinski dodecahedron with unit edge length are given by:

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

Gallery

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External links

• Wikipedia Contributors. "Bilinski dodecahedron".
• Weisstein, Eric W. "Bilinski Dodecahedron" at MathWorld.
• McCooey, David. "Bilinski's Dodecahedron"