Diamond cuboctahedron
The (small) rhombic cuboctahedron is a polyhedron ( polyhedron ) that is one of the Archimedean solids . It is made up of 8 equilateral triangles and 18 squares . Three squares and one triangle each form a corner of the room .
Each 8 edges of the diamond cuboctahedron form the edges of a regular octagon . There are a total of six such independent, equilateral octagons in this polyhedron.
The name of the rhombicuboctahedron is based u. a. on the fact that 12 of the 18 squares are congruent with the 12 rhombuses of a circumscribed rhombic dodecahedron . The body that is dual to the rhombic cuboctahedron is the deltoidal icositetrahedron .
Formulas
Sizes of a rhombic cuboctahedron with edge length a | |
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Volume ≈ 8.71 a 3 |
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Surface area ≈ 21.46 a 2 |
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Umkugelradius ≈ 1.4 a |
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Edge ball radius ≈ 1.31 a |
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Diagonal angle ( square - square ) = 135 ° |
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Diagonal angle (square - trine ) ≈ 144 ° 44 ′ 8 ″ |
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Corners solid angle ≈ 1.108 π |
Trivia
In engineering, the shape is used for components that serve as nodes for the construction of metal space framework .
The rhombic cuboctahedron forms the base of the Moravian Star, which is widely used as an Advent and Christmas star .
The National Library of Belarus is built in the shape of a rhombicuboctahedron.
See also
Web links
- Eric W. Weisstein : Rhombicuboctahedron . In: MathWorld (English).