# Bilinski dodecahedron

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Bilinski dodecahedron
Rank3
Elements
Faces8 + 2 + 2 golden rhombi
Edges4 + 4 + 4 + 8
Vertices2 + 4 + 4 + 4
Measures (edge length 1)
Central density1
Abstract & topological properties
Flag count96
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryK3, order 8
ConvexYes
NatureTame

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:

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