The Elongated Pentagonal Bipyramid
The elongated pentagonal bipyramid is the 16th Johnson solid (J16). It has 12 vertices, 25 edges, and 15 faces (10 equilateral triangles and 5 squares).
The elongated pentagonal bipyramid can be constructed by attaching two pentagonal pyramids to a pentagonal prism. Its name describes its relation to the pentagonal bipyramid: inserting a pentagonal prism between the two constituent pentagonal pyramids to make the bipyramid longer.
Projections
Here are some views of the elongated pentagonal bipyramid from various angles:
| Projection | Envelope | Description |
|---|---|---|
 |
Regular pentagon | Top view. |
 |
Hexagon | Front view. |
 |
Hexagon | Side view. |
Coordinates
The Cartesian coordinates of the elongated pentagonal bipyramid with edge length 2 are:
- (0, 0, ±(1+√((10−2√5)/5)))
- (√((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 elongated pentagonal bipyramid occurs as cells in the following CRF polytopes:
