Small stellated dodecahedron
The Dodekaederstern (also called Small Sterndodekaeder ) is a regular polyhedron is one of the Keplerian star bodies; It is bounded by 60 equilateral triangles. The star body is characterized by the equality of all dihedral angles - both inside and outside - of 116.57 ° from.
Formation & Properties
If all edges of a pentagonal dodecahedron extends both beyond its corners to be cut five of them at one point, then a Dodekaederstern, which can be thought of as the dodecahedron with twelve mounted pyramids. The prongs of the Dodekaedersterns form the vertices of a regular icosahedron with the side length.
The Dodekaederstern is the circumscribed body of twelve mutually intersecting pentagrams, which are coincident with the boundary faces of a dodecahedron. Inside the Dodekaedersterns are 20 equilateral triangles, cut surfaces whose side length is equal to the diagonal of the pentagram, and a span the Great icosahedron.
- The surfaces of the dodecahedron and Ikosaederstern are equal, the latter includes the smaller volume.
- Pentakisdodekaeder and Dodekaederstern are topologically equivalent.