Small spangled dodecahedron

In Geometry, the small dodecahedron spangled is a Solide of Kepler-Poinsot . It is one of the four regular polyhedrons not-convex. It is composed of 12 pentagrammic faces, with five pentagrams meeting at each top.

The 12 tops coincide with the localizations for a Icosaèdre. The 30 edges are divided by the Grand icosahedron.

He is regarded as the first of the three stellations of the dodecahedron.

If the pentagrammic faces are regarded as five triangular faces, it shares same topological surface as the Pentakidodécaèdre, but with isosceles triangular faces larger.

Like a stellation

It can also be built like the first of the four stellations of the dodecahedron, and referred like the model of Wenninger [W20].

References

Magnus Wenninger : Polyhedron Models 1974 ISBN 0-521-09859-9
H.S. Mr. Coxeter: The Fifty-Nine Icosahedra 1938 ISBN 0-387-90770-X

External bonds

: 3 stellations of the dodecahedron

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