If the edges pair with each triangle's vertex and if they are perpendicular to the base, it is a right triangular prism.

Examples are some of the Johnson solids, the truncated right triangular prism, and Schönhardt polyhedron.

[4] If the base is equilateral and the lateral faces are square, then the right triangular prism is semiregular.

This means that a triangular prism has regular faces and has an isogonal symmetry on vertices.

[6] The three-dimensional symmetry group of a right triangular prism is dihedral group D3h of order 12: the appearance is unchanged if the triangular prism is rotated one- and two- thirds of a full angle around its axis of symmetry passing through the center's base, and reflecting across a horizontal plane.

The gyrobifastigium is constructed by attaching two triangular prisms along one of its square faces.

As a result, the two bases are not parallel and every height has a different edge length.

Given that A is the area of the triangular prism's base, and the three heights h1, h2, and h3, its volume can be determined in the following formula:[14]

This way, one of its bases rotates around the prism's centerline and breaks the square faces into skew polygons.

Each square face can be re-triangulated with two triangles to form a non-convex dihedral angle.

[15] As a result, the Schönhardt polyhedron cannot be triangulated by a partition into tetrahedra.

[16] It is named after German mathematician Erich Schönhardt, who described it in 1928, although the related structure was exhibited by artist Karlis Johansons in 1921.

Thorold Gosset identified this series in 1900 as containing all regular polytope facets, containing all simplexes and orthoplexes (equilateral triangles and squares in the case of the triangular prism).

The triangular prism exists as cells of a number of four-dimensional uniform 4-polytopes, including: