Grünbaum's new rhombic hexecontahedron

Grünbaum's new rhombic hexecontahedron is a isohedral polyhedron with 60 golden rhombus faces.

Grünbaum's new rhombic hexecontahedron
Rank3
Elements
Faces60 golden rhombi
Edges60 + 60
Vertices20 + 20 + 12
Related polytopes
Convex hullRhombic triacontahedron
Convex coreRhombic triacontahedron
Abstract & topological properties
Flag count480
Euler characteristic-8
OrientableYes
Genus5
Properties
SymmetryH3, order 120
Flag orbits4
ConvexNo

Construction edit

 
Grünbaum's new rhombic hexecontahedron as a stellation of the rhombic triacontahedron

Grünbaum's new rhombic hexecontahedron is a stellation of the rhombic triacontahedron. The stellation is given by the following stellation diagram:
  
The left shows the new faces in red and the old face in yellow, and the right shows the interior of the polyhedron with an even-odd-filling in green and exterior in dark blue.

Related polytopes edit

Grünbaum's new rhombic hexecontahedron is related to the rhombic hexecontahedron which is another stellation of the rhombic triacontahedron with 60 golden rhombus faces.

Bibliography edit

  • Grünbaum, Branko (1996a), A New Rhombic Hexecontahedron-Once More (PDF)
  • Grünbaum, Branko (1996b), A New Rhombic Hexecontahedron (PDF)