Small triambic icosahedron
- Small triambic icosahedron
In geometry, the small triambic icosahedron is the dual to the uniform small ditrigonal icosidodecahedron. It is composed of 20 intersecting isogonal hexagon faces. It has 60 edges and 32 vertices, and Euler 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 an icosahedron and adding short triangular pyramids. With the proper pyramid height this figure becomes a Catalan solid by the same name and the dual of the truncated dodecahedron).
The nonconvex uniform polyhedra great stellated dodecahedron and great 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 the icosahedron, and given as Wenninger model index 26.
This stellation is a popular subject for construction in modular origami, often made of thirty Sonobe 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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