Compound of cube and octahedronTypeCompoundCoxeter diagram ∪ Stellation corecuboctahedronConvex hullRhombic dodecahedronIndexW43Polyhedra1 octahedron1 cubeFaces8 triangles6 squaresEdges24Vertices14Symmetry groupoctahedral (Oh)
The compound of cube and octahedron is a polyhedron which can be seen as either a polyhedral stellation or a compound. Construction
The 14 Cartesian coordinates of the vertices of the compound are. 6: (±2, 0, 0), ( 0, ±2, 0), ( 0, 0, ±2) 8: ( ±1, ±1, ±1)
As a compound
It can be seen as the compound of an octahedron and a cube. It is one of four compounds constructed from a Platonic solid or Kepler-Poinsot polyhedron and its dual.
It has octahedral symmetry (Oh) 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.
As a stellation
It is also the first stellation of the cuboctahedron and given as Wenninger model index 43.
It can be seen as a cuboctahedron with square and triangular pyramids added to each face.
The stellation facets for construction are:
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