The Hexagonal Prism
The hexagonal prism is a 3D uniform polyhedron bounded by 8 polygons (2 hexagons and 6 squares), 18 edges, and 12 vertices. It is the extrusion of the hexagon into 3D.
Attaching a triangular cupola to a hexagonal prism produces the elongated triangular cupola (J18), a Johnson solid. Attaching a second triangular cupola produces either the elongated triangular orthobicupola (J35) or the elongated triangular gyrobicupola (J36), depending on whether the second cupola is aligned or rotated with respect to the first, respectively.
- The augmented hexagonal prism (J54);
- The parabiaugmented hexagonal prism (J55);
- The metabiaugmented hexagonal prism (J56);
- The triaugmented hexagonal prism (J57).
In order to be able to identify the hexagonal 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:
Hexagon-centered parallel projection.
Parallel projection centered on a vertical edge.
Square-centered parallel projection.
Vertex-centered parallel projection.
The Cartesian coordinates of the hexagonal prism, centered on the origin and having edge length 2, are:
- (±√3, ±1, ±1)
- (0, ±2, ±1)
The hexagonal prism occurs as cells in the following 4D uniform polytopes:
- The runcitruncated 5-cell;
- The omnitruncated 5-cell;
- The runcitruncated tesseract;
- The runcitruncated 16-cell;
- The omnitruncated tesseract;
- The runcitruncated 24-cell;
- The omnitruncated 24-cell;
- The runcitruncated 600-cell;
- The omnitruncated 120-cell.
It also occurs in a number of CRF polychora, including (but not limited to):