The Pentagonal Prism
The pentagonal prism is a 3D uniform polyhedron bounded by 7 polygons (2 pentagons and 5 squares), 15 edges, and 10 vertices. It may be considered to be the extrusion of the pentagon.
The pentagonal prism can be augmented by a square pyramid to form the augmented pentagonal prism (J52), a Johnson solid. A second square pyramid can be added at a nonadjacent position to produce the biaugmented pentagonal prism (J53).
The dual of the pentagonal prism is the pentagonal bipyramid. Not to be confused with its topological Johnson solid analogue J13, but a nonJohnson pentagonal bipyramid among the uniform duals which include the Catalan solids.
Projections
In order to be able to identify the pentagonal prism in various projections of 4D objects, it is useful to know how it appears from various viewpoints. The following are some of the commonlyencountered views:
Projection  Envelope  Description 

Regular pentagon  Parallel projection centered on a pentagonal face. 

Rectangle  Parallel projection centered on a vertical edge. 

Rectangle  Parallel projection parallel to a square face. The left edge of the projection envelope is the image of a square face. 
Coordinates
The Cartesian coordinates of the pentagonal prism, centered on the origin and having edge length 2, are:
 (√((10+2√5)/5), 0, ±1)
 (√((5−√5)/10), ±φ, ±1)
 (−√((5+2√5)/5), ±1, ±1)
where φ=(1+√5)/2 is the Golden Ratio.
Occurrences
The pentagonal prism occurs in the following 4D uniform polytopes:
 The runcinated 120cell;
 The cantellated 600cell;
 The cantitruncated 600cell;
 The runcitruncated 600cell;
 The 5,10duoprism;
 The 5,20duoprism.
The pentagonal prism also occurs in the following CRF polychora: