The Triangular Prism

The triangular prism is a simple 3D uniform polyhedron bounded by 2 triangular faces and 3 squares. It has 9 edges and 6 vertices. It may be considered to be the extrusion of the triangle.

The triangular

Two triangular prisms can be glued together at their square faces in gyro orientation to produce a gyrobifastigium (J26), a Johnson solid:

Two triangular prisms
glued together to make a gyrobifastigium


In order to be able to identify the triangular prism in various projections of 4D objects, it is useful to know how it appears from various viewpoints. The following are some of the commonly-encountered views:

Projection Envelope Description

Parallel projection centered on a triangular face.


Parallel projection centered on a vertical edge.


Parallel projection parallel to a square face. The left edge of the projection is the image of a square face.

Non-uniform pentagon

Vertex-centered parallel projection.


The Cartesian coordinates of the triangular prism, centered on the origin and having edge length 2, are:


The triangular prism is a very versatile polyhedron that occurs in many 4D uniform polytopes, including:

It also occurs in many CRF polychora, including (but not limited to):

Last updated 07 Mar 2018.

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