Penetration of five octahedra

Composite of five octahedra

The penetration of five octahedra found in the icosidodecahedron create this star body.

The penetration of five octahedra represents a star body that arises from a suitable combination of five octahedra found in the icosidodecahedron .

This polyhedron was first described in 1876 by the German mathematician Edmund Hess (1843-1903).

The star body is composed of 120 irregular triangles and has as many points as the icosidodecahedron has corners, namely 30. The icosidodecahedron forms the convex envelope of this star body.

Dihedral angle

The surface angle of the star body is just as large as that of a single octahedron (see there ).

≈ 109 ° 28 ′ 16 ″

${\displaystyle \cos \,\alpha =-{\frac {1}{3}}}$

See also

• Penetration of five tetrahedra
• Penetration of five cubes
• Hexakis icosahedron

Web links

Commons : composite of five octahedra  - collection of images, videos and audio files

• Eric W. Weisstein : composite of five octahedra . In: MathWorld (English).