The Gyroelongated Pentagonal Pyramid
The gyroelongated pentagonal pyramid is the 11th Johnson solid (J11). It has 11 vertices and 16 faces (15 equilateral triangles and 1 pentagon).
The gyroelongated pentagonal pyramid can be constructed by attaching a pentagonal pyramid to a pentagonal antiprism. It can also be constructed by deleting a single vertex from the icosahedron, and so can also be called the monodiminished icosahedron.
Projections
Here are some views of the gyroelongated pentagonal pyramid from various angles:
| Projection | Envelope | Description |
|---|---|---|
 |
Regular decagon | Top view. |
 |
Pentagon | Side view. |
 |
Pentagon | Front view. |
Coordinates
The Cartesian coordinates of the gyroelongated pentagonal pyramid with edge length 2 are:
- (0, 0, A + √((10-2√5)/5)
- ±(B, 0, A)
- ±(C, ±φ, A)
- ±(-D, ±1, A)
where
| A | = | √((5+√5)/10) |
| B | = | √((10+2√5)/5) |
| C | = | √((5-√5)/10) |
| D | = | √((5+2√5)/5) |
| φ | = | (1+√5)/2 |
