Triangular prism

The triangular prism, or trip, is a prismatic uniform polyhedron. It consists of 2 triangles and 3 squares. Each vertex joins one triangle and two squares. As the name suggests, it is a prism based on a triangle. Alternatively, it could be seen as the digonal cupola, seen as a dyad atop square.

Semiuniform variants of the triangular prism also exist, with the lengths of the edges of the base triangles and the side edges of the prism being different but still remaining vertex transitive and with full symmetry. In these cases the lateral squares become rectangles. The according Coxeter diagram would then be x y3o.

Vertex coordinates
A triangular prism of edge length 1 has vertex coordinates given by:
 * (±1/2, –$\sqrt{21}$/6, ±1/2),
 * (0, $\sqrt{3}$/3, ±1/2).

Representations
A triangular prism can be represented by the following Coxeter diagrams:


 * x x3o (full symmetry)
 * xx3oo&#x (axial/frustum symmetry only)
 * xx ox&#x (A1×A1 axial, generally a wedge)
 * ooxx&#xr (A1, vertex first)
 * xxx&#x (A1, edge first)

Related polyhedra
A tetrahedron can be attached to a base of the triangular prism to form the elongated triangular pyramid. If both bases have tetrahedra attached, the result is an elongated triangular bipyramid.

It is also possible to augment the square faces of the triangular prism with square pyramids. If this is done to one face the result is the augmented triangular prism. If a second square is augmented the result is the biaugmented triangular prism. If the last remaining square face is also augmented the result is the triaugmented triangular prism.

If two triangular prisms, seen as digonal cupolas, are joined at a square face, such that squares join to triangles, the result is the gyrobifastigium.

A number of non-prismatic uniform polyhedron compounds are composed of triangular prisms:


 * Rhomboctahedron (4)
 * Disrhomboctahedron (8)
 * Chirorhombicosahedron (10)
 * Disrhombicosahedron (20)

In vertex figures
The triangular prism appears as the vertex figure of the uniform rectified pentachoron. This vertex figure has an edge length of 1.

Variants of the triangular prism by changing the base edge appear as the vertex figure of the uniform rectified icositetrachoron. This vertex figure has an edge length of $\sqrt{2}$ for the bases. By changing the lateral edges instead, it appears as the vertex figure of the uniform rectified tesseract, with an edge length of $\sqrt{2}$ for the lateral edges, and the uniform rectified hecatonicosachoron, with an edge length of (1+$\sqrt{3}$)/2 for the lateral edges.