Truncated dodecahedron
The truncated dodecahedron is a polyhedron ( polyhedron ) that is created by blunting the corners of a pentagon dodecahedron and is one of the Archimedean solids . Instead of the 20 corners of the dodecahedron there are now just as many equilateral triangles ; the pentagons of the dodecahedron become regular decagons .
The polyhedron that is dual to the truncated dodecahedron is the triacis icosahedron .
Formulas
Sizes of a truncated dodecahedron with edge length a | |
---|---|
volume | |
Surface area | |
Umkugelradius | |
Edge ball radius | |
1. Diagonal angle ( decagon - decagon ) ≈ 116 ° 33 ′ 54 ″ |
|
2. Diagonal angle (decagon - trigon ) ≈ 142 ° 37 ′ 21 ″ |
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3D edge angle (decagon trigon) ≈ 159 ° 5 ′ 41 ″ |
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Corners solid angle ≈ 1.2323 π |
Web links
Commons : Truncated Dodecahedron - collection of images, videos and audio files
Wiktionary: truncated dodecahedron - explanations of meanings, word origins, synonyms, translations
- Eric W. Weisstein : Truncated Dodecahedron . In: MathWorld (English).