Rectified prism

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.

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

Elements

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

Forms

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

n	3	4	5	6	7	n
Image
Net
Related		Cuboctahedron

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

Dual

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
Image
Net
Related		Rhombic dodecahedron

See also

• Rectified antiprism

External links

• Conway Notation for Polyhedra Try: aPn and jPn, where n=3,4,5,6... example aP4 is a rectified square prism, and jP4 is a joined square prism.