Hollowed out dodecahedron

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3D view of a 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

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

Commons : Hollowed out dodecahedron  - collection of images, videos and audio files

Individual evidence

  1. The Fifty Nine Icosahedra (Eng.)