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A right prism is a prism in which the joining edges and faces are perpendicular to the base faces. [5] This applies if and only if all the joining faces are rectangular. The dual of a right n-prism is a right n-bipyramid. A right prism (with rectangular sides) with regular n-gon bases has Schläfli symbol { }×{n}.
General cuboids have many different types. When all of the rectangular cuboid's edges are equal in length, it results in a cube, with six square faces and adjacent faces meeting at right angles. [1] [3] Along with the rectangular cuboids, parallelepiped is a cuboid with six parallelogram. Rhombohedron is a cuboid with six rhombus faces.
The relations can be made apparent by examining the vertex figures obtained by listing the faces adjacent to each vertex (remember that for uniform polyhedra all vertices are the same, that is vertex-transitive). For example, the cube has vertex figure 4.4.4, which is to say, three adjacent square faces. The possible faces are 3 - equilateral ...
This more restrictive type of cuboid is also known as a rectangular cuboid, right cuboid, rectangular box, rectangular hexahedron, right rectangular prism, or rectangular parallelepiped. [5] Polyhedron: Flat polygonal faces, straight edges and sharp corners or vertices: Small stellated dodecahedron: Toroidal polyhedron: Uniform polyhedron
A rectangular cuboid is a convex polyhedron with six rectangle faces. These are often called "cuboids", without qualifying them as being rectangular, but a cuboid can also refer to a more general class of polyhedra, with six quadrilateral faces. [1] The dihedral angles of a rectangular cuboid are all right angles, and its opposite faces are ...
A rhombicosahedron shares its vertex arrangement with the uniform compounds of 10 or 20 triangular prisms. It additionally shares its edges with the rhombidodecadodecahedron (having the square faces in common) and the icosidodecadodecahedron (having the hexagonal faces in common).
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.
In geometry, the pentagrammic prism is one of an infinite set of nonconvex prisms formed by square sides and two regular star polygon caps, in this case two pentagrams. It is a special case of a right prism with a pentagram as base, which in general has rectangular non-base faces. Topologically it is the same as a convex pentagonal prism.