Set of rectified prisms

Rectified pentagonal prism
Conway polyhedron notation aPn
Faces 2 n-gons
n squares
2n triangles
Edges 6n
Vertices 3n
Symmetry group Dnh, [2,2n], (*22n), order 4n
Rotation group Dn, [2,n]+, (22n), order 2n
Dual polyhedron Joined prism
Properties convex

In geometry, a rectified prism (also rectified bipyramid) is one of an infinite set of polyhedra, constructed as a rectification of an n-gonal prism, truncating the vertices down to the midpoint of the original edges. In Conway polyhedron notation, it is represented as aPn, an ambo-prism. The lateral squares or rectangular faces of the prism become squares or rhombic faces, and new isosceles triangle faces are truncations of the original vertices.

Elements

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An n-gonal form has 3n vertices, 6n edges, and 2+3n faces: 2 regular n-gons, n rhombi, and 2n triangles.

Forms

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The rectified square prism is the same as a semiregular cuboctahedron.

n 3 4 5 6 7 n
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Cuboctahedron

Rectified star prisms also exist, like a 5/2 form:

 

Dual

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Set of joined prisms
 
Joined pentagonal prism
Conway polyhedron notation jPn
Faces 3n
Edges 6n
Vertices 2+3n
Symmetry group Dnh, [2,2n], (*22n), order 4n
Rotation group Dn, [2,n]+, (22n), order 2n
Dual polyhedron Rectified prism
Rectified bipyramid
Properties convex

The dual of a rectified prism is a joined prism or joined bipyramid, in Conway polyhedron notation. The join operation adds vertices at the center of faces, and replaces edges with rhombic faces between original and the neighboring face centers. The joined square prism is the same topology as the rhombic dodecahedron. The joined triangular prism is the Herschel graph.

n 3 4 5 6 8 n
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Rhombic dodecahedron

See also

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