Compound of cube and octahedron

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Compound of cube and octahedron
Compound of cube and octahedron.png
Type Compound
Coxeter diagram CDel nodes 10ru.pngCDel split2-43.pngCDel node.pngCDel nodes 01rd.pngCDel split2-43.pngCDel node.png
Stellation core cuboctahedron
Convex hull Rhombic dodecahedron
Index W43
Polyhedra 1 octahedron
1 cube
Faces 8 triangles
6 squares
Edges 24
Vertices 14
Symmetry group octahedral (Oh)

This polyhedron can be seen as either a polyhedral stellation or a compound.

As a compound[edit]

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.

As a stellation[edit]

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:

First stellation of cuboctahedron trifacets.pngFirst stellation of cuboctahedron square facets.png