The Elongated Square Bipyramid
The elongated square bipyramid is the 15th Johnson solid (J15). It has 10 vertices, 20 edges, and 12 faces (8 equilateral triangles and 4 squares).
The elongated square bipyramid can be constructed by attaching two square pyramids to a cube. Its name describes its relation to the octahedron, regarded as the square bipyramid: inserting a cube between the two constituent square pyramids to make the bipyramid longer.
Projections
Here are some views of the elongated square bipyramid from various angles:
Projection  Envelope  Description 

Square  Top view. 

Hexagon  Side view. 

Hexagon  Diagonal side view. 
Coordinates
The Cartesian coordinates of the elongated square bipyramid with edge length 2 are:
 (0, 0, ±(1+√2))
 (±1, ±1, ±1)
Occurrences
Due to its relation with the octahedron as a partial Stott expansion, the elongated square bipyramid features as cells in a number of CRF polychora, including (but not limited to):