Compound of cube and octahedron: Difference between revisions

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{{Short description|Polyhedral compound}}

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!bgcolor=#e7dcc3 colspan=2|Compound of cube and octahedron

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|bgcolor=#e7dcc3|[[Symmetry group]]||[[Octahedral symmetry|octahedral]] (''O''_''h'')

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[[File:Bronze mace head from Galicia.jpg|thumb|Medieval [[Mace (bludgeon)|mace]] head]]

ThisThe '''compound of cube and octahedron''' is a [[polyhedron]] which can be seen as either a polyhedral [[stellation]] or a [[Polyhedron compound|compound]].

==Construction==

The 14 [[Cartesian coordinate]]s of the vertices of the compound are.

: 6: (±2, 0, 0), ( 0, ±2, 0), ( 0, 0, ±2)

: 8: ( ±1, ±1, ±1)

== As a compound ==

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It has [[octahedral symmetry]] ('''O'''_''h'') and shares the same vertices as a [[rhombic dodecahedron]].

This can be seen as the three-dimensional equivalent of the compound of two squares ({8/2} "[[octagram]]"); this series continues on to infinity, with the four-dimensional equivalent being the [[compound of tesseract and 16-cell]].

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| footer = A cube and its [[dual polyhedron|dual]] octahedron

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The stellation facets for construction are:

:[[Image:First stellation of cuboctahedron trifacets.png|240px]][[Image:First stellation of cuboctahedron square facets.png|240px]]

== See also ==

* [[Compound of two tetrahedra]]

* [[Compound of dodecahedron and icosahedron]]

* [[Compound of small stellated dodecahedron and great dodecahedron]]

* [[Compound of great stellated dodecahedron and great icosahedron]]

==References==