- Small triambic icosahedron
In

geometry , the**small triambic icosahedron**is the dual to the uniformsmall ditrigonal icosidodecahedron . It is composed of 20 intersecting isogonal hexagon faces. It has 60 edges and 32 vertices, andEuler characteristic of −8.If the intersected hexagonal faces are divided and new edges created, this figure becomes the

triakis icosahedron . The descriptive name "triakis icosahedron" represents a topological construction starting with anicosahedron and adding short triangular pyramids. With the proper pyramid height this figure becomes aCatalan solid by the same name and the dual of thetruncated dodecahedron ).The nonconvex uniform polyhedra

great stellated dodecahedron andgreat dodecahedron , as viewed as surface topologies, can also be constructed as icosahedron with pyramids, the first with much tall pyramids, and the second with inverted ones.**As a stellation**This figure is also the first

stellation of theicosahedron , and given as Wenninger model index 26.This stellation is a popular subject for construction in

modular origami , often made of thirtySonobe units.**References*** (p. 46, Model "W"

_{26}, triakis icosahedron)

* (pp. 42–46, dual to uniform polyhedron "W"_{70})

*Citation | last1=Coxeter | first1=Harold Scott MacDonald | author1-link=Harold Scott MacDonald Coxeter | last2=Du Val | first2=P. | last3=Flather | first3=H. T. | last4=Petrie | first4=J. F. | title=The fifty-nine icosahedra | publisher=Tarquin | edition=3rd | isbn=978-1-899618-32-3 | id=MathSciNet | id = 676126 | year=1999 (1st Edn University of Toronto (1938))**External links***

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2010.*

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