Small triambic icosahedron

Small triambic icosahedron
Type Dual uniform polyhedron
Index DU30, 2/59, W26
Elements
(As a star polyhedron)		 F = 20, E = 60
V = 32 (χ = −8)
Symmetry group icosahedral (Ih)
Dual polyhedron small ditrigonal icosidodecahedron
Stellation diagram Stellation core Convex hull

Icosahedron
Pentakis dodecahedron

In geometry, the small triambic icosahedron is a star polyhedron composed of 20 intersecting non-regular hexagon faces. It has 60 edges and 32 vertices, and Euler characteristic of −8. It is an isohedron, meaning that all of its faces are symmetric to each other. Branko Grünbaum conjectured that it is the only Euclidean isohedron with convex faces of six or more sides, but the small hexagonal hexecontahedron is another example.

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