Truncated hexahedron
The truncated hexahedron is a polyhedron ( polyhedron ) that is created by blunting the corners of a cube (hexahedron) and is one of the Archimedean solids . Instead of the eight corners of the cube, there are now eight equilateral triangles ; the six squares of the cube become regular octagons .
If you put the cut corner pieces together again in a suitable way, you get an octahedron . From this it follows that the entire space can be completely filled ( parquetted ) using truncated hexahedra and octahedra (each with the same edge length) : eight truncated hexahedra enclose exactly one octahedron.
The body that is dual to the truncated hexahedron is the triakis octahedron .
Formulas
Sizes of a truncated hexahedron with edge length a | |
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volume | |
Surface area | |
Umkugelradius | |
Edge ball radius | |
1. Diagonal angle ( octagon - octagon ) = 90 ° |
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2. Diagonal angle (octagon - trine ) ≈ 125 ° 15 ′ 52 ″ |
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Surface-edge angle ≈ 144 ° 44 ′ 8 ″ |
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Corners solid angle ≈ 0.8918 π |
Web links
Commons : Truncated Hexahedron - Collection of images, videos and audio files
Wiktionary: truncated hexahedron - explanations of meanings, word origins, synonyms, translations
- Eric W. Weisstein : Truncated hexahedron . In: MathWorld (English).