Hollowed out dodecahedron
The hollowed out dodecahedron is a concave polyhedron that is composed of 60 equilateral triangles and is one of the star bodies .
20 of the total of 32 corners are identical to those of a dodecahedron , which forms the convex hull of the star body. The other 12 corners on the inside form the corner points of an icosahedron .
Emergence
Twelve pentagonal pyramids ( ), whose base surfaces are congruent with the boundary surfaces of the dodecahedron, are subtracted from a dodecahedron (side length ) .
Furthermore, this polyhedron is one of the 59 possible “starings” of the icosahedron (Bez .: Ef1g1 ).
Related polyhedra
Dodecahedron (convex hull)
Icosahedron (core)
Equivalent to the hollowed out dodecahedron - in terms of number of faces, corners and edges - are the pentakis dodecahedron and the dodecahedron star .
Formulas
Sizes of a hollowed out dodecahedron with edge length a | ||
---|---|---|
volume | ||
Surface area | ||
Pyramid height | ||
Icosahedron edge length | ||
1. Face angle ≈ 138 ° 11 ′ 23 ″ |
||
2. Face angle ≈ 41 ° 48 ′ 37 ″ |
Web links
- Eric W. Weisstein : Icosahedron Stellations . In: MathWorld (English).
Individual evidence
- ↑ The Fifty Nine Icosahedra (Eng.)