SMALL STELLATED DODECAHEDRON

In geometry, the 'small stellated dodecahedron' is a Kepler-Poinsot polyhedron. It is one of four nonconvex regular polyhedra. It is composed of 12 pentagrammic faces, with five pentagrams meeting at each vertex.
It shares the same vertex arrangement as the convex regular icosahedron. It also shares the same edge arrangement as the great icosahedron.
It is considered the first of three stellations of the dodecahedron.
If the pentagrammic faces are considered as 5 triangular faces, it shares the same surface topology as the pentakis dodecahedron, but with much taller isosceles triangle faces.

A transparent model of the small stellated dodecahedron (See also )

Contents

As a stellation

In art

References

External links

As a stellation

It can also be constructed as the first of four stellations of the dodecahedron, and referenced as Wenninger model [W20].
The stellation facets for construction are:
:

In art

A small stellated dodecahedron is seen featured in Gravitation by M. C. Escher.

References

★ Polyhedron Models, , Magnus, Wenninger, Cambridge University Press, 1974, ISBN 0-521-09859-9

★ The Fifty-Nine Icosahedra, , H. S. M., Coxeter, Springer-Verlag, New York, Berlin, Heidelberg, 1938, ISBN 0-387-90770-X

External links

★ MathWorld: Small stellated dodecahedron

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★ MathWorld: Three stellations of the dodecahedron

★ Bronze sculpture of small stellated dodecahedron