Grünbaum's new rhombic hexecontahedron

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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

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

Construction[edit | edit source]

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 | edit source]

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 | edit source]

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