The Pentagonal Bipyramid
The pentagonal bipyramid is the 13th Johnson solid (J13). It has 7 vertices, 15 edges, and 10 faces (10 equilateral triangles).
The pentagonal bipyramid can be constructed by attaching two pentagonal pyramids to each other at their bases.
Projections
Here are some views of the pentagonal bipyramid from various angles:
| Projection | Envelope | Description |
|---|---|---|
 |
Regular pentagon | Top view. |
 |
Rhombus | Side view. |
 |
Tetragon | Front view. |
Coordinates
The Cartesian coordinates of the pentagonal bipyramid with edge length 2 are:
- (0, 0, ±√((10−2√5)/5))
- (√((10+2√5)/5), 0, 0)
- (√((5−√5)/10), ±φ, 0)
- (−√((5+2√5)/5), ±1, 0)
where φ=(1+√5)/2 is the Golden Ratio.
Occurrences
The pentagonal bipyramid occurs as cells in some CRF polychora, including (but not limited to):
