The Decagonal Prism

The decagonal prism is a 3D uniform polyhedron bounded by 2 decagonal faces and 10 squares. It has 30 edges and 20 vertices. It may be considered to be the extrusion of the decagon.

The decagonal

A decagonal prism can be attached to a pentagonal cupola (J5) to form an elongated pentagonal cupola (J20), or to a pentagonal rotunda (J6) to form an elongated pentagonal rotunda (J21).

The elongated pentagonal
cupola The elongated pentagonal


In order to be able to identify the decagonal 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
Regular decagon

Decagon-centered parallel projection.


Parallel projection centered on a vertical edge.


Square-centered parallel projection.


Vertex-centered parallel projection.


The Cartesian coordinates of the decagonal prism, centered on the origin and having edge length 2, are all changes of sign of:

where φ=(1+√5)/2 is the Golden Ratio.


The decagonal prism occurs in the following uniform polychora:

Last updated 11 Apr 2018.

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