The Gyroelongated Square Pyramid
The gyroelongated square pyramid is the 10th Johnson solid (J10). It has 9 vertices, 20 edges, and 13 faces (12 equilateral triangles and 1 square)
The gyroelongated square pyramid can be constructed by attaching a square pyramid to a square antiprism.
Attaching a second square pyramid to the other side of the antiprism produces the gyroelongated square bipyramid (J17).
Projections
Here are some views of the gyroelongated square pyramid from various angles:
| Projection | Envelope | Description |
|---|---|---|
 |
Regular octagon | Top view. |
 |
Pentagon | Side view. |
 |
Pentagon | Diagonal side view. |
 |
Pentagon | 22.5° side view. |
Coordinates
The Cartesian coordinates of the gyroelongated square pyramid with edge length 2 are:
- (0, 0, √2 + 1/∜2)
- (0, ±√2, 1/∜2)
- (±√2, 0, 1/∜2)
- (±1, ±1, −1/∜2)
