The Elongated Pentagonal Pyramid
The elongated pentagonal pyramid is the 9th Johnson solid (J9). It has 11 vertices, 20 edges, and 11 faces (5 equilateral triangles, 5 squares, and 1 pentagon).
The elongated pentagonal pyramid can be constructed by attaching a pentagonal pyramid to a pentagonal prism.
Attaching a second pentagonal pyramid to the other end of the pentagonal prism produces the elongated pentagonal bipyramid (J16).
Projections
Here are some views of the elongated pentagonal pyramid from various angles:
| Projection | Envelope | Description |
|---|---|---|
 |
Regular pentagon | Top view. |
 |
Pentagon | Side view. |
 |
Pentagon | Front view. |
Coordinates
The Cartesian coordinates of the elongated pentagonal pyramid 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.
