The Cuboctahedron


The cuboctahedron is a uniform polyhedron bounded by 6 squares and 8 triangles. It is edge-uniform, and its two kinds of faces alternate around each vertex, so it is also a quasi-regular polyhedron. It may be constructed by truncating a cube or an octahedron at the midpoints of its edges (this process is known as rectification).

The
cuboctahedron

The cuboctahedron can be bisected by a plane parallel to two opposite triangular faces to produce the triangular cupola (J3), a Johnson solid.

Two triangular cupola
forming a cuboctahedron

Projections

In order to be able to identify the cuboctahedron in various projections of 4D objects, it is useful to know how it appears from various viewpoints. The following are some of the commonly-encountered views:

Projection Envelope Description
Square

Parallel projection centered on a square face.

Regular hexagon

Parallel projection centered on a triangular face.

Hexagon

Vertex-first projection.

Hexagon

Edge-first projection.

Coordinates

The Cartesian coordinates of the cuboctahedron, centered on the origin and having edge length 2, are all permutations of coordinates and changes of sign of:

Occurrences

The cuboctahedron occurs as cells in a variety of 4D uniform polytopes:


Last updated 25 Feb 2014.

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