The Elongated Square Bipyramid

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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):

• The octa-augmented runcinated tesseract;
• The octa-augmented runcitruncated 16-cell.