Rhombicuboctahedron
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| - | In [[geometry]], the '''rhombicuboctahedron'''[http://commons.wikimedia.org/wiki/File:Leonardo_polyhedra.png], or '''small rhombicuboctahedron''', is an [[Archimedean solid]] with eight [[triangle|triangular]] and eighteen [[square (geometry)|square]] faces. There are 24 identical vertices, with one triangle and three squares meeting at each. Note that six of the squares only share vertices with the triangles while the other twelve share an edge. The [[polyhedron]] has [[octahedral symmetry]], like the [[Cube (geometry)|cube]] and [[octahedron]]. Its [[dual polyhedron|dual]] is called the [[deltoidal icositetrahedron]] or trapezoidal icositetrahedron, although its faces are not really true [[trapezoid]]s. | + | In [[geometry]], the '''rhombicuboctahedron'''[http://commons.wikimedia.org/wiki/File:Leonardo_polyhedra.png], or '''small rhombicuboctahedron''', is an [[Archimedean solid]] with eight [[triangle|triangular]] and eighteen [[square (geometry)|square]] faces. |
| - | The name ''rhombicuboctahedron'' refers to the fact that 12 of the square faces lie in the same planes as the 12 faces of the [[rhombic dodecahedron]] which is dual to the [[cuboctahedron]]. ''Great rhombicuboctahedron'' is an alternative name for a [[truncated cuboctahedron]], whose faces are parallel to those of the (small) rhombicuboctahedron. | + | [[Johannes Kepler]] in [[Harmonices Mundi]] (1618) named this polyhedron a ''rhombicuboctahedron'', being short for ''truncated cuboctahedral rhombus'', with ''cuboctahedral rhombus'' being his name for a [[rhombic dodecahedron]]. |
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| - | It can also be called an '''[[Expansion (geometry)|expanded]] cube''' or ''[[Cantellation (geometry)|cantellated]] cube'' or a ''cantellated octahedron'' from truncation operations of the [[uniform polyhedron]]. | + | |
| The shape is found in [[Jacopo de' Barbari]]'s painting ''[[Portrait of Luca Pacioli]]''. | The shape is found in [[Jacopo de' Barbari]]'s painting ''[[Portrait of Luca Pacioli]]''. | ||
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In geometry, the rhombicuboctahedron[1], or small rhombicuboctahedron, is an Archimedean solid with eight triangular and eighteen square faces.
Johannes Kepler in Harmonices Mundi (1618) named this polyhedron a rhombicuboctahedron, being short for truncated cuboctahedral rhombus, with cuboctahedral rhombus being his name for a rhombic dodecahedron.
The shape is found in Jacopo de' Barbari's painting Portrait of Luca Pacioli.
See also
Unless indicated otherwise, the text in this article is either based on Wikipedia article "Rhombicuboctahedron" or another language Wikipedia page thereof used under the terms of the GNU Free Documentation License; or on research by Jahsonic and friends. See Art and Popular Culture's copyright notice.
![[1]](http://commons.wikimedia.org/wiki/File:Leonardo_polyhedra.png){kind=link}