geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

, a rectified prism (also rectified bipyramid) is one of an infinite set of

polyhedra In geometry, a polyhedron (plural polyhedra or polyhedrons; ) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron is the convex hull of finitely many points, not all on t ...

, constructed as a

rectification Rectification has the following technical meanings: Mathematics * Rectification (geometry), truncating a polytope by marking the midpoints of all its edges, and cutting off its vertices at those points * Rectifiable curve, in mathematics * Recti ...

of an ''n''-gonal

prism Prism usually refers to: * Prism (optics), a transparent optical component with flat surfaces that refract light * Prism (geometry), a kind of polyhedron Prism may also refer to: Science and mathematics * Prism (geology), a type of sedimentary ...

, truncating the vertices down to the midpoint of the original edges. In

Conway polyhedron notation In geometry, Conway polyhedron notation, invented by John Horton Conway and promoted by George W. Hart, is used to describe polyhedra based on a seed polyhedron modified by various prefix operations. Conway and Hart extended the idea of using op ...

, 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 In geometry, an isosceles triangle () is a triangle that has two sides of equal length. Sometimes it is specified as having ''exactly'' two sides of equal length, and sometimes as having ''at least'' two sides of equal length, the latter versio ...

faces are truncations of the original vertices.

Elements

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

Forms

The ''rectified square prism'' is the same as a semiregular

cuboctahedron A cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces. A cuboctahedron has 12 identical vertices, with 2 triangles and 2 squares meeting at each, and 24 identical edges, each separating a triangle from a square. As such, it ...

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

Dual

The dual of a ''rectified prism'' is a joined prism or joined bipyramid, in

. 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 In geometry, the rhombic dodecahedron is a convex polyhedron with 12 congruent rhombic faces. It has 24 edges, and 14 vertices of 2 types. It is a Catalan solid, and the dual polyhedron of the cuboctahedron. Properties The rhombic dodecahedro ...

. The ''joined triangular prism'' is the

Herschel graph In graph theory, a branch of mathematics, the Herschel graph is a bipartite undirected graph with 11 vertices and 18 edges. It is a polyhedral graph (the graph of a convex polyhedron), and is the smallest polyhedral graph that does not have a Ha ...

External links

Conway Notation for Polyhedra
Try: aP''n'' and jP''n'', where n=3,4,5,6... example aP4 is a rectified square prism, and jP4 is a joined square prism. Polyhedra {{polyhedron-stub

Elements

Forms

Dual

See also

External links