Great icosahedron

Great icosahedron

In geometry, the great icosahedron is a Kepler-Poinsot polyhedron. It is one of four nonconvex regular polyhedra. It is composed of 20 intersecting triangular faces, with five triangles meeting at each vertex in a pentagrammic sequence.

It shares the same vertex arrangement as the regular convex icosahedron. It also shares the same edge arrangement as the small stellated dodecahedron.

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As a stellation

It is also a stellation of the icosahedron, counted by Wenninger as model [W41] and the 16th of 17 stellations of the icosahedron and 7th of 59 stellations by Coxeter.

The stellation facets for construction are::

References

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*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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** mathworld | urlname = IcosahedronStellations| title = Fifteen stellations of the icosahedron


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